Which is otherwise known as Gresham's Law. People will save Bitcoin and spend fiat, with bad money driving good money out of circulation under your hypothetical circumstances
I heard Gresham's "law" is for commodity money with intrinsic value, like tobacco. Mr. Free to choose said (sorry, I forgot the link/source) in the past tobacco was widely used in the US as money, and in the end, people spent the low-quality tobacco and saved the high-quality tobacco. This behavior droves out high-quality tobacco out of circulation
It is the effect that counts here
And this effect is present even when two fiat currencies are competing which don't have intrinsic value (other than transnational utility). You may argue that it is not Gresham's Law, and you would probably be right, technically speaking. However, if there is such a thing as "bad money driving good money out of circulation" (irrespective of the form of money, i.e. whether it is sea shells, hard currency, fiat, or whatever), we have to deal with it somehow and name it