Saxony has a stronger economy than Brandenburg and a higher population density.
Brandenburg and Mecklenburg have the lowest population densities in Germany.
Despite a smaller economic base Brandenburg managed to field larger Armies.
The city of Leipzig already was an important trading place for Central Europe.
That's definitely true, Saxony compares very favorably to Brandenburg and East Prussia-- Prussia just taxed its commoners enough (buying off the Junkers by taxing them less and giving them state salaries) to build a bigger army. Frederick the Great, like Alexander the Great, was able to built on the achievements of his father. Although, that army has to actually win to be a good investment (because even if you win, you will probably lose a ton of money and
tens if not hundreds of thousands of men)-- if it loses, then you'll seek other means of protecting your independence (which is why many other small states within the HRE preferred vassalage and gifts, instead of arming to the teeth). And Prussian victory often benefited from foreign assistance-- the Seven Years War, in which it fought alone except for British subsidies against France, Austria, and Russia, nearly broke it. It was nearly a bridge too far, Russian coins were minted for occupied Konigsberg-- and these were respected more than the debased Prussian coins. Few states took the rickety, uncertain Prussian route because these are the sorts of situations you could find yourself in by design or accident, scraping the metal off coins and just hoping you can hold out longer than your enemies. But then, Tsar Peter III (and his decision was upheld by Catherine II, even if she used the deal as an excuse to overthrow her husband) gave East Prussia back free of charge-- because Prussia would be more useful to Russia as a fellow partitioner of Poland. Elizabeth (
who had no children), who took East Prussia in the first place, thought she could arrange some deal where she'd give it to Poland and get some other territory from Poland-- but I'm sure she wouldn't have gotten as much as Catherine later got in the First Partition, and then the two after that.
Saxony, like Prussia, can only do so much on its own even if it operates at maximum efficiency. So where are its friends and how could they feasibly deliver subsidies, troops, or other aid in a time of crisis? Saxony being landlocked, their friends are to be found on land-- like Austria, which wants Saxony to do what it did OTL, be Catholic and function as a Habsburg proxy in the war against French backed candidates for the Polish throne.
Coal becomes important in the 19 century. The nearest important coal fields which Saxony could gain are in Southern Silesia. A competently lead Saxon Army could conquer Silesia in an alternate war of Austrian succession.
From the vantage of the late 1600s, it's a long and bloody century until then. Poland did not live to see the 19th century, and Saxony was lucky to survive--
Metternich promised Saxony to Prussia in October 1814, trading Saxony for Westphalia was entirely Prussia's choice.
A coup to dismantle and radically alter the politics of the Polish-Lithuanian Commonwealth is an interesting idea. However a foreign king would face a lot of resistance, and any noble alliance against him would easily get foreign support.
Maybe a somewhat richer Saxony enters a personal union with Poland at a later date, after an alternate first partition, with Poland already weakened. Then maybe a strong reformed Saxon army would maybe strong enough to enforce radical reforms. Desperation could convince more nobles that serious reforms are indeed necessary.
I guess it would be weird for a foreign ruler to do all that for their new country but-- Catherine II was 100% German. And her husband and predecessor Peter III was 50% Russian (through his mother, the elder daughter of Peter the Great) but he was raised in Kiel and identified with German culture.
Peter the Great's intended heir Alexei was... a real piece of work, and then his younger brother died at four-- so Russia's rulers after Peter were Catherine I (Peter's Polish wife), Peter II (Peter's grandson through Alexei), Anna I (Peter's half-brother's daughter), Ivan VI (great-grandson of Peter's half-brother), Elizabeth I (Peter's younger daughter), Peter III (Peter's grandson through his elder daughter), and then Catherine II (no blood connection to Peter whatsoever). After her came her son Paul I (Peter I's great-grandson through Peter III), then his son Alexander I, and so Russia returned in the 1800s to father-son succession as God intended.
But through most of the 1700s (Peter I died in 1725, Catherine II in 1796) yhe succession is jumping all around the family tree, and it's drawing in more and more of those foreign spouses, friends, and lovers that Peter was so intent on having all the king's men (and women) marry and associate with-- these people who Russians were supposed to absorb culture from or whatever ended up drawn closer and closer to the center of power by the chaotic succession. It sounds like a recipe for disaster.
But for some reason it wasn't-- probably because whoever was on top was expected to feel some ownership over the whole enterprise, to occupy the space which Ivan IV and Peter I had carved out for the benefit of future monarchs-- to sit on the old greats' throne and make use of their spies. If a new monarch could overcome whatever coups were mounted against them, they would face little opposition in the day to day. And Catherine II responded to that by taking ownership-- first deposing her husband for being a "Germanophile" and then showing how a real Tsarina does it. Namely, they don't do it alone-- Catherine continued efforts going back to Peter I to produce and employ talented personnel from Russia and abroad. But that multinational harvest of talent needed some form of executive direction, and a Tsar(ina) could certainly be a chief executive.
Now I understand why "Poland should be more like Tsarist Russia and Bourbon France" doesn't seem like an obvious conclusion-- after all we usually bash both of those governments in order to justify the revolutions that ended them. But both of them very consistently accomplished a lot, even if the problems they could not deal with sapped the public's trust in them-- something they could have used in the crises that finally ended them. And it may seem somehow unpalatable that the unique and fascinating government and philosophy of the PLC should be abandoned wholesale for another boring autocracy-- surely the right solution would be a compromise of liberty and executive direction, deliberation and the final word. But that's always been a moving target, it would be very difficult to hit even if it was still-- why would Poland get it right on the first try when even England, even America, required several attempts? England overshot and got the Protectorate, America undershot and got the Articles of Confederation. Of course America's isolation let it bumble around in peace-- the hellish competition of early modern Europe will not allow undershooting. But, even an overshoot can be course corrected by subsequent events-- the heritage of the Golden Liberty may be all the more beloved for a brief absence, in which it is remembered fondly but evaluated critically.
So how is Saxony supposed to fit into all of this? Saxony's job from the Habsburg perspective is to keep Poland pro-Habsburg and keep... well, keep Stanislaw Leszczynski out along with whoever is backing him (Sweden the first time in the 1700s, France the second time in the 1730s). That's a very vague mission and Saxony has carte blanche-- Austria won't interrupt them as long as the nightmare scenario of a French-Polish invasion of Germany doesn't happen. The trouble is that Saxony-Poland has another customer it must satisfy, Russia-- and Russia would love nothing more (it has no more desirable direction of expansion) than the Baltic and the lands of old Kyivan Rus'. The Saxons Augustus II and III had one contest each with Stanislaw Leszczynski-- in both contests they were backed by Russia, which made decisive contributions to their victory. This isn't to say Russia has some surefire method of selecting only bad rulers for Poland-- they did select Stanislaw August Poniatowski, only for him to be a reformist. No, Russia's method really only consists of waiting and seeing-- and once they have seen enough, marching tens of thousands of troops in to sabotage reform even if they were the ones who let the reformist become king in the first place. And then there's the Prussian jackal-- although it never acted against Poland alone except in the 1790s, when Russia acts against Poland Prussia will usually be right beside it.
Taking the above into account, Saxony only has to keep Austria on side while enduring Russia-- not necessarily defeating it, but enduring it. When Russia invades (there is no "if") Poland should be at a state of enough readiness and resolve that it could keep the government intact (even if it needs to move to a safe place within Poland or across the border into Saxony) while punishing and delegitimizing whatever collaborator confederation Russia organizes-- assassinations, propaganda (the printing press?), stealing the regalia, whatever. That level of Polish strength might make Austria nervous, but by using the same strength to defeat Prussia Saxony can defend itself and convince Austria that it is of no threat for Habsburg primacy in Germany. And that should be it-- France, Sweden, or Britain can cause trouble but they're just flashes in the pan, their contributions are only grafted onto the more consistent influence of the Three Partitioners.
Could a Saxon king have done that? Well, it doesn't look like either of the Wettins ever tried, or maybe they tried and realized it was impossible. But if they had the resolve of Joseph II Habsburg, maybe things could have been different for Saxony and Poland alike? Especially in that period 1740-1760 in which Saxon kings ruled Poland and it should have been very plain that just having Poland wouldn't be enough to protect Saxony from Prussia, if even Austria was losing to them.
