I don't understand how a CBDC can completely forbid its users from buying bitcoin, unless there has to be a justification for every transaction happening, which besides utopian is neither going to work in practice.
It's very easy actually...Have you seen how Market Pass works? It only allows transactions to stores that sell food. And that's not even CBDC, it's still fiat.
Now imagine ECB launching CBDC and making a smart contract that forbids your wallet from sending money to well-known CEXes like Coinbase, Binance, Kraken etc.
Of course people will be ingenious to find other -roundabout- solutions: I can buy a highly-sought product (let's say a PS5 or an iPhone*) with CBDC and then sell it in the black market for BTC.
But that means the CBDC -> BTC exchange rate won't be very favorable... in fact, I don't even expect 1:1 parity (despite ECB enforcing it) between the physical (zero limitations) and the digital euro (CBDC).
* assuming you will still be allowed to buy these products, because even that is not 100% certain:
https://www.theverge.com/2023/6/14/23760879/sony-ps5-cloud-streaming-games-test
https://www.theverge.com/2022/3/24/22994814/apple-iphone-hardware-subscription-bundle-report
Maybe they will tell you that owning these devices emits way too much CO2, therefore they would quickly deduct your carbon credits.
