The problem is that your ordinary citizens do not know the difference between the two. If CBDC is "government supported," then it must be legal, right? Educating the public in some way about actual value support seems to be the only way to ensure that CBDC has nowhere to go.
It shouldn't matter as long as we understand the difference.
Sooner or later news will start flowing about money automatically seized from criminals' wallets, then about money seized from correct citizens by various mistakes of the govt or automation... and while some will say "I have nothing to hide", others will understand the difference.
And there's something more: Bitcoin's scarcity will keep making it a good investment, not only a censorship free coin.