While I don't claim to be overly knowledgeable on this era, It always seemed to me that Napoleon was in the unenviable position where just about all of Europe hates him. The fact that there were so many coalitions between often enemy countries against him shows that. And while France was still arguably the main continental power at the time, only enhanced by Napoloeon's leadership and effective military reforms, it was not equal to the rest of Europe. We hadn't yet reached World War levels of recruitment and army size where massive numbers of fighting age men were recruited. Prussia and the Austria were able to replace their lost soldiers using British funds. Except now, they weren't armies using outdated equipment and led by generals stuck in 18th century military tactics.
The main problem is that as just about every other main power was against him, Napoleon had to keep his enemies on their knees. If he hadn't quickly smacked down Russia for its defiance of his Continental System, what's to stop Prussia and Austria from similarly acting against him? The way I see it, Napoleon had the choice between attacking Russia to try and defeat his opponent's piecemeal or sit back and allow his enemies to gather together and create another coalition against him. A Coalition this time leading modern armies led by experienced generals both used to his tactics and adopting them for themselves. The possibility of an alt-Waterloo is highly possible.
That is if they even decided outright invasion was necessary. Wars are expensive. If the German countries and Austria decided to heavily restrict trade with France, alongside Britain's continued naval blockades, and you are looking at major economic trouble for France. The Continental System would be turned against him.
The real problem I always thought about Napoleon is strategic, not tactical. Napoleon was amazing at winning battles, but he never had a truly viable strategy for winning the wars in the long term. He beat his enemies, they signed a treaty, they raised new armies, he beat them again, they signed another treaty, they raised yet another army, etc. There was no genuine pacification of his foes. His very existence made him an existential enemy of the heads of state during the time, his diplomacy wasn't that vaunted besides the big stick kind, and industrialization hadn't yet reached the point that that by the end of a failed war an entire countries' economy was in the toilet. France under Napoleon found itself facing basically every other major European power, and France simply didn't have the numbers and industry to beat them all in the long term. He was great in the short term, great in the medium term, but gradually collapsed in the long term.
Remember the first coalitions were against Revolutionary France. So it's really the fact that the surrounding nations are dynastic monarchies and therefore democracies and/or democratically born pseudo-monarchies are existential threats because their mere existence (let alone dominance) provides a very worrying example to the people if you happen to be a dynastic monarch.
As to your identification of the coalition-victory-treaty-new Coalition pattern, I agree it's the problem, but I don't see it as his strategic shortcoming. He understood the fact that Britain generated/funded every one of these. He understood that without naval control he couldn't stop Britain from doing that. He tried improving the navy, and he tried making a public issue of British honour, but the RN saw to the first and the new propogandic British press saw to the latter. So what could he do? He tried to address Britain indirectly through economic pressure via Continental, and that's what Russia was about. It's not like he was Hulk smash, he really was pretty exhausted by war, but the system of the day relied on a kind of honour re:treaties and Britain kept basically saying (after the fact) that honour only exists between dynastic monarchies, therefore it's just paper, funding another coalition and invading.
But say we break the pattern where he has control. He says Britain never honours treaties, their word is useless, therefore after beating another coalition he refuses to give them peace and...then what?