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.
maybe if the supply grew over time, it would just offset the price going up to some degree. that's about it. so people that want bitcoin price to "pump" they're always strong proponents for the fixed supply. now you know why.
Example, current Bitcoin price inflated by Tether printer with no real backing.
what about the joe biden printer? he's printing money out of thin air like CRAZY.
HOWEVER
bitcoin is not a peg of fiat
bitcoin has its own economics.. EG mining cost has a factor that give bitcoin a base wholesale value layer below market rate to support the market bottoms.
but mining costs have to be paid using fiat. so they are based on fiat. if the fiat has inflation then everything costs more. mining equipment, electricity, etc. so the bottom line goes up. so bitcoin is a peg of fiat in a way. it's not independent of it.