The inflation due to bitcoin mining is already smaller than other systems that are widely considered stable. Note that I don't think bitcoin will actually be stable, but I think inflationary pressures are almost insignificant as a factor that would drive it to collapsing.

For bitcoin, 90% of all bitcoin has already been mined. So the remaining dilution for all time is in total just about 11%, and the current annual rate is 1.8% inflation. Compare this to gold, which has 2% inflation and no max supply. There are also technological innovations that could inflate gold much faster, e.g. asteroid mining. Compared to USD as measured by CPI is 8%, and the Fed's own target for CPI inflation is 2% annually, so this is much higher than bitcoin and also unbounded total dilution.

Don't confuse money supply growth and inflation. (Unless you're a monetarist, of course, but their doctrine has been quite convincingly refuted over the last decade and a half.) Inflation is change in the price of real goods.

BTC experiences 1.7% money supply growth p.a. until the next halving, and it had deflation on the way up to $60k. BTC had 100% inflation since then, obviously, way worse than fiat.

Fiat had massive money supply growth since the GFC, but virtually no inflation until now (which can be explained by supply chain problems due to COVID, war, and too loose fiscal policy (Biden's stimulus arguably too large, after Obama's was too small)).