The problem is more than just CBDC vs BTC & Cryptos - the problem is the public is lazy and will take whatever path requires the least of them and appears to give them the most.
There will most certainly be a battle and I suspect it will last a very long time.
Most people will fall for the conveniences compared to the value they might get, with that in mind, it is necessary to improve the user experiences of using bitcoins or altcoins. That is the way forward so people could utilize cryptocurrencies wider, besides adoption. I think at the end of the day, people will choose things that help their life easier, there will be a ratio between conveniences and value, and people would compromise on things that gives them the most benefit.
Once the implementation or the law is established, it will be then applied and force the citizen to follow it. So government forcing its citizen to use CBDC is a natural course of events.
But I think there is a chance that Bitcoin and CBDC will co-exist along the way.
Forcing people to use CBDC seems unwise and authoritarian, even the current societies that favour cashless payment are still keeping cash as an option.