Thus, bad coins ended up dominating the market, and good coins disappeared.
Could something like this happen to Bitcoin?
I don't really get the ideas of bad coins and good coins here from Gresham's Law. Bitcoin is magic in a way that if you have private key, you can spend bitcoins belong to that private key. Bad or good coins, you all can spend it anytime by signing your transaction with private key and waiting for confirmations from Bitcoin miners.
In Bitcoin, there is only tainted coin and non-tainted coin but it's vague overlap between them in practice too. Bitcoin is fungible with a smallest unit is satoshi and it's really hard to know that your bitcoin is completely non-tainted, clean and not related to any past mixing activities. In addition, as a Bitcoin user I really don't care about that too.
In other words, are people starting to want to save their BTC coins so much that their value is lost?
It can help price to increase, not to decrease. Principle of Supply and Demand says it, and I agree it works for Bitcoin too.
Two articles I like