The loot did not exclusively belong to a general. At least officially. Of course a lot of embezzlement happened, when it came to loot. But not on that of a big scale. Not counting Julius Caesar in Gaul. But if the republic allows such "Caesars", the republic cannot survive anyways. So if Crassus sacks Ctesiphon, and the senate allows him to keep the parthian treasury, the republic does not survive. But the initial assumption is, that the republic survives.
So it is hard to believe, that a single roman gets rich enough to build the Collosseum. It was build with the jewish temple treasury and about 20.000 jewish enslaved prisoners of war. Even Crassus would have had to calculate intensively, to make that happen.
It is also hard to believe, that the roman republican senate authorizes a censor to spend that much money out of the aeraerium saturni on a colosseum. Well, you need more than one Censor, because the project takes more than 5 years. But thats a minor issue.
On the other hand: if this mean and selfish aristocratic roman republic senate, does not change dramatically, by whatever reasons, the republic cannot survive anyways. However, I don't believe, that a republican senate would agree to projects on a very big scale, if there is no absolute need to do so.
PS: one possibility: Crassus dies without an heir after a succesful parthian campaign, which makes him without doubt even richer, and hands down his total property to the republic with the condition to use this money for the collosseum. This is possible by roman law. And Crassus' assets should have been huge enough (some 100 Mio. HS). But why should he do that?