How do Bitcoiners audit supply of Bitcoin? You probably just run a node to do this exactly like every Bitcoin and Monero user. No Bitcoiner is taking advantage of it's transparency/simple math to scrutinize the whole blockchain every block to make sure every single output equals all inputs. So in practice what is the difference?
Monero audits supply using bulletproofs and pedersen commitments. It is not obscure it is well established and sound cryptography from the 80s, but admittedly more complex than bitcoins simple math.
An exploited inflation bug would be equally catastrophic once it happened to either Bitcoin or Monero. Attackers have the advantage. There is no good solution to fix this without hurting other users on either Bitcoin or Monero.
Trivia: Did you know there was a hidden inflation bug in Bitcoin only an anonymous user knew? They couldve easily exploited it, but very luckily they were an honest actor who secretly let the devs know (who couldve also decided to exploit it). If they did exploit it, how would detectable inflation help after the fact? It wouldnt.