We have three things in your post. They are btc, fiat and CBDCs. Btc is decentralized and runs on blockchain, CBDC is centralized and runs on blockchain and the fiat is decentralized and does not run on blockchain.
If you want to make comparison is should be on centralize and decentralized.
If it is like that, bitcoin is different from the rest two.
But if you talk about competition, CBDC should be in competition with fiat because they have the same parents which is government. Bitcoin is different and bitcoin is liberty.
There is no such comparison between the decentralized one to centralized form of the market as they are totally a different alternative to fiat money(local currency). And why Bitcoin couldn't overthrow fiat (local currency) for the reason that people just consider this an investment like bonds and any businesses. To earn some profit from investing in Bitcoin make people encourage, not the way we could use to pay bills, buy stuff, or anything as we do like with fiat.
Therefore, the government does not need to be afraid that actually legalizing Bitcoin for payments will threaten the existence of fiat. Because as
you explained, most people are more comfortable using fiat to pay bills and buy daily necessities. Moreover, with the price of Bitcoin which is
very volatile, it would be better if it is used for investment, maybe if we want to send money abroad using Bitcoin is a good choice too.
In conclusion, Bitcoin and fiat were created not to compete, but to complement each other. So Bitcoin and fiat if used by humans will make
financial transactions much more effective, because both Bitcoin and fiat have their own advantages and disadvantages. Humans desperately need
both to live a much better life.