We already discussed this matter in the past (
here, for your reading pleasure)
Someone has come up with exactly the same reason there, namely, Thiers' Law. However, Gresham's Law, or its proper extension, still persists if we consider two currencies, which are freely exchangeable at market rates. Thiers' Law basically describes a situation when one currency fails as money, i.e. no one wants to accept it. In that case people simply refuse to transact in it, and thus no free exchange is possible. Obviously, this is not the case here. Bitcoin is a worthy speculative asset, and it is not a good idea overall to spend your capital on everyday needs, Gresham's Law or otherwise (read, it is Thiers' Law which is not applicable here)
But Gresham’s law cannot be applied to “two currencies, which are freely exchangeable at market rates”. That’s is an incorrect interpretation of the law’s setting
I know what Gresham’s Law is about. That's why I mentioned its extension
If we create a setting where two currencies (BTC and a national fiat) are widely accepted as a medium of exchange (in other words, are equally liquid), BTC will destroy the fiat currency, which happens according to Thiers' Law. I actually modelled that scenario in Part 1, you must have missed it
You can freely trade Bitcoin for fiat and vice versa
So why does it not destroy fiat? Maybe exactly because of the Gresham’s Law extension, that bad money drives out good money from circulation? It's ironic that you try to appeal to the natural outcome of this extension (Bitcoin not being widely used as a means of payment) to support the opposite claim, that Bitcoin would dispatch fiat currencies. However, no one can stop us from analyzing your proposition theoretically, "in vitro". Could you name just one killer feature of Bitcoin that would render the fiat currency useless as a currency?