You have to realize that bitcoin is still very volatile and still a growing technology that needs more massive adoption as we have been seeing. So some people are by nature conservative, because of this they trust what they can feel and touch and something that appears stable but actually dying in the real sense. Not everyone can cope with a huge risk and volatility.
Do you mean people will trust Bitcoin if the price becomes stable? I don't think it is a reason why people more trust USD. We know that Bitcoin use is still quite limited, cannot be fully used for various purposes in all countries in the world. In my country, people are only allowed to use Bitcoin as a digital asset. And there are too many critics about the uncertainty about Bitcoin. This makes people prefer to choose what common people use nowadays. If Bitcoin is getting more familiar and it can be fully accepted both for digital investment and payment purposes, people may choose Bitcoin.
It couldnt really become stable no matter what and it would be always that volatile because it is a market which do involves buyers and sellers which it is would be always volatile no matter what and this
had been the primary reason on why people do love out the most on hanging out on this market because of that very sole reason and of course people would always trust up fiat no matter what
and would end up accumulating fiat no matter what and of course they would really be trusting it out which it is just normal to have those kind of mindset.