Is it, though? The vast majority of Rome's wars had ended with a treaty of alliance, not political destruction
They were low scale conflicts, tough, involving entities with a fairly small regional expense. From the moment Rome had to deal with regional-scale entities, the city essentially elected to destroy it and ally/submit with the remnants, roughly since the defeat of Samnite confederation. It's how the conflict with Syracuse, Carthage, Macedonia was dealt in this period.
You're right that the alliance/tributary system was largely used with cities and tribal entities, but they weren't considered as existential or strategical threats.
Moreover, insofar as they even practiced it, this all-or-nothing mentality was not exactly unique to the Romans.
The difference was that Rome went trough this systematically with most of the state it encountered : the practice of compromised peace which dominated hellenistic diplomacy (without being systematical itself) knew there a significant departure.
The Athenians fought on after the city had been destroyed in the Persian invasion,
It was essentially a come-back for the sack of Sardis, tough, and not really something Persians relied on generally.
Corinth and Thebes wanted Athens razed to the ground at the end of the Peloponnesian War
And the practice of non-annhiliation (partly born out of a necessity of hegemonic balance) still prevailed nevertheless.
and Alexander did not stop until he had subjugated the entirety of the Achaemenid empire.
Which doesn't really was an annihilation of Persian state or empire, and rather its takeover by Alexander.
Admittedly, that's a bit beside the point; Hannibal's actions -building alliances with Capua et al and Macedon- point towards an intent to contain Rome in the post war world by forming his own Italian league to replace the Roman confederation and counterbalance his city's arch rival in the West.
Alliance with Capua was essentially a way to weaken Rome and prevent it to really pose a naval threat (both military and commercial), rather than expect a containement of the city trough Capuan regional dominance : it was clear from the beggining that the Campanian city couldn't fulfill its ambitions to dominate southern Italy (nor most of important cities as Locri) and hannibal simply didn't interfered with local politics while it definitely weakened the strategical importance of the region.
As for Macedonia, the relatively supple alliance only appeared as Rome refused to negotiate, and Carthaginians didn't do much on this regard.
Both were rather opportunistic agreements without real incidence for either Hannibal or Carthage's ambitions in western Med.
The relations with Syracuse are rather more interesting on this regard, notably because it was part of a direct Carthagian sphere of influence, using the sicilian city as a strategical ally into depriving Rome of any presence or influence in Sicily.
For one, it would be very interesting to compare this allegedly distinctive style of war with the large numbers of Spanish fighters in Hannibal's army, who mostly seemed content to engage in long sieges.
While Gauls had a significant advance in defensive siege tactics, the lack of evidence of besieging attacking tactics is to be pointed. As far as it's theorized, it was probably limited to basic poliorcetic with initial tentatives, and then surrounding the fortification to deprive besiegees of reinforcement and supplies.
On the other hand, we know that Celtiberians more often practiced siege warfare (altough it might be partly a source bias, there's still archeological lack of evidence in Gaul), but the tradition of mercenariship in Mediterranean basin and especially under Carthaginians in this period are to be tied with siege tactics borrowed from their employer or hegemon. Note that after the IIIrd century, Celtiberians didn't went trough a huge departure from usual wait and see habits on siege warfare.
https://www4.uwm.edu/celtic/ekeltoi/volumes/vol6/6_2/gorbea_lorrio_6_2.pdf
Second, even if loot was the primary motivation, can you think of a better prize than Rome itself?
Loot wasn't really this obvious of a prime motivation : at least for Cisalpine Gaul, which formed an important part of Gallic armies of Hannibal, there was the matter of pushing back Roman encrochement of their lands.
Note that the clear material gain that was expected wasn't specifically loot itself, but payment and compensation from Carthaginian in exchange of their service (Gaistai mercenaries fighting in Cisalpina and Italy worked along these lines). It doesn't mean that loot wasn't expected as well, but compensation was more usual when it comes to mercenary armies rather than expeditions as happening in Balkans decades before.
Do you have any solid evidence that Gauls lack the patience for a <40 day siege, or is this pure speculation?
You probably know that theories on Gallic warfare are partly speculation from archeological and historical evidence, because we don't have much to grab onto safe partial evidence. Note that absence of solid and certified evidence that Gauls didn't this much went trough sieges doesn't mean that the contrary is proven by default.
There's no much archeological evidence that would point Gauls used a set of active siege tactics, and their general practice seems to have been (like in High Middle-Ages, interestingly) to rather deprive the besieged from reinforcement and supplies, waiting for surrender. The inability to adapt themselves to hellenistic-romans siege warfare in the IInd to Ist century, while we know some of the biggest fortifications found in Gaul didn't have an obvious military role (as the second wall of Bibracte) is interesting.
Of course, it doesn't mean that it was systematical, and Gauls might have made contact with mediterranean active siege warfare in the frames of the Carthaginian army. But I doubt they would have played something else than an auxiliary role at this point, just like Celtiberians doesn't seem to have played a major role in Hannibal's army in Saguntum. The problem being that such active tactics imply and involves sophisticated siege engines, themselves implying genie and specialized logistical support.
Besides the siege of Capitolum by Brennos, which is at least partly legendary and to be taken with particular caution (especially about the length of the siege and the scale of the destruction), we don't have account of the length of sieges in Gallic warfare that wouldn't involve service in hellenistic armies, where their role was fairly minor.
Alain Debyer's
Les Gaulois en Guerre is pretty much interesting on thie matter of warfare in Gaul, if you can find it.
Eventually, while I agree with you that
@FillyofDelphi might have underestimated the capacity of Gallic mercenaries in siege warfare, I doubt it would be something more than in an auxilary role, with Hannibal possibly lacking specialized troops at this point as much as he lacked siege engines.
In the context of -215, I'm not sure a large army could live on the land waiting from the long months of depriving Romans from supply and reinforcement would be feasible.
Note that Hannibal could always count on Romans believing it would be, tough, and pressure them this way.