What do you mean by "fiat price"?There's no such term as fiat price.There's only fiat money.
Do you mean the USD/EUR price of bitcoin?
Anyway,the so called "stable coins" is sooner or later disappear and their creators will cashout a lot of money.
Their fiat reserves(if they really have such reserves) are going to decrease a lot,because everyone will be buying btc and altcoins.
I don't think so. Stable coins do have their own advantages making them useful in bull and bear markets which is why they won't disappear anytime inspite of the controversies they get embroiled in regularly.
For example, Tether is still in the top 10 of CMC rankings despite being hit by a controversy recently.