If fixed supply can be infinitely inflated (when it comes to price) and thus creating a bubble that can burst, it is not being different from supply that is not fixed.
Example, current Bitcoin price inflated by Tether printer with no real backing.
[img]https://i.imgflip.com/8ppmmm.jpg[/img
Fixed supply of BTC doesn't matter, when the price can be infinitely inflated by Tether printer.
FIAT has no real backing either. The only difference between tether and usd is the issuer. USDT is issued by bitfinex, USDT is issued by the FED. Both are backed by nothing. Till now, the authorities didn't care if USDT was backed by USD or not so why should we care if the real owner and the issuer of the FIAT (the FED) doesn't?
Fixed supply of BTC kind of matters but it is not always a good thing. Let's say it has its advantages. Would you rather prefer to invest in a non-fixed supply coin like ethereum? That's way more messed up.