tldr: Immediately trying to destroy the blood has clear advantages, but also has some drawbacks and isn't as trivial an exercise as it first appears.
This is a very good question, and @Rahil's answer is excellent. The OP has asked:
Why Kvothe didn't even try to destroy the blood sample Ambrose had,
almost literally at the moment he and his friends realized it was
malfeasance? It should actually be a trivial exercise... Why Kvothe could not reverse the direction and using sympathy target the blood Ambrose smeared on the mummet?
The blood wasn't "smeared on the mommet"
Ambrose mixed the blood into the clay (or wax, or some other material) and made the mixture into a mommet. To the best of our knowledge of sympathy, this makes it impossible to create a sympathetic link to the blood1, just as you would be unable to make a link to a specific protein or chemical in the blood. At this point, Kvothe's choices were to target the whole mommet (as he ends up doing), or to do nothing. He doesn't have an option to destroy just the blood.
Destroying the mommet is not quick or easy
With the "destroy the blood" option off the table, Kvothe (via Devi) is forced to destroy the whole mommet. This means taking the time to make and try different materials. Furthermore, the mommet turns out to be clay, and clay doesn't burn. Perhaps the momment would crack, but all Ambrose needs to do is glue it back together and he's back in business. Sim is actually the one who destroys the mommet, not with fire and sympathy but with hobnail boots. If you try leave the clay mommet hot enough, for long enough, to be sure that it is totally destroyed, you start to worry that...
Ambrose could re-establish the link
A critical part of Kvothe's plan is that Fela distracts Ambrose while Kvothe and company break into his rooms. Suppose that Ambrose was paying attention during the several minutes that Kvothe tries to destroy the mommet (cycling through different materials, keeping it hot enough for long enough). Then, when the mommet is good and hot, he re-establishes the link to Kvothe. Suddenly, the harder you work to destroy the mommet, the more danger Kvothe is in. As it turns out, Kvothe's alar is probably strong enough to destroy the mommet and protect himself at the same time, but busting out this sort of top-tier sympathetic ability presents a new danger...
Kvothe doesn't want Ambrose to know who's blood he's got
Ambrose doesn't know that he has Kvothe's blood. He doesn't even know that he has a sympathist's blood. If Kvothe tries to uses sympathy to destroy the mommet, Ambrose is one step closer to figuring out that Kvothe is the one who broke into his rooms, at which point he doesn't need the mommet. He could bring Kvothe up on charges and have him thrown out of the university.2 If Kvothe uses sympathy to destroy the mommet, he needs to make sure that he doesn't leave any evidence behind.
Kvothe wants to be 100% certain that the mommet is gone
This is the single most important factor in Kvothe's decision to break into Ambrose's rooms. Arcanists don't automatically know what is happening at the other end of their link. Using sympathy, Kvothe could never be sure if he has destroyed the mommet, or just got it really hot and then stopped. Ambrose could have protected the mommet with a gram or kept it in a sympathy-powered icebox. Kvothe doesn't even know for sure that there is only one mommet. There could be dozens. Until he breaks into Ambrose's rooms4, he can't be sure that all of his blood is safe again. And as long as he's not sure, destroying the mommet doesn't even help his situation. If there's even a 1% chance that Ambrose preserved a sample of blood for future use, Kvothe needs to keep his defenses up 24/7. Destroying the momment doesn't do much good unless you know that it's been destroyed.
In his answer, @Radhil correctly states that:
[R]esponsible arcanists - pretty much anyone not Ambrose - aren't
going to just send energy anywhere without knowing or having a very
good idea what the consequences are going to be.
Kvothe is clever, talented, and legendarily virile3, but he is not, and has never been, a responsible arcanist. Personally, I do not believe that preventing collateral damage was a decisive factor in Kvothe's plan. But it might have been important to getting Wil, Sim, Fela, and Mola onboard to help.
Should Kvothe have immediately tried to destroy the mommet? Trying to do so was not trivial and not risk-free. But personally, I think that yes, he should have tried. In my analysis, the benefits of having the mommet destroyed immediately outweigh the risks of possibly failing to destroy it, maybe setting an inn on fire, and Ambrose somehow tracing the whole debacle back to him. In Kvothe's analysis of the situation, it was better to wait.
1The exact limitations of forming sympathetic links to parts of objects aren't clear. While dueling in Sympathy class, Kvothe makes a link between a piece of straw and a candle's wick, not a link between a piece of straw and the entire candle. Perhaps it would have been possible to boil away the blood and leave the clay, but Kvothe doesn't try.
2It is left as an exercise to the reader to imagine how Ambrose would prove that Kvothe is a thief, without simultaneously exposing himself to charges of malfeasance.
3At least in stories where he is also the narrator.
4And really, not even then. Hence the gram.