Can you trade private coins on any CEX that operates within the EU? All my local CEXs removed trading with private coins a few years ago, not because some law came into force prohibiting it, but because they were guided by the recommendation of the regulatory agency.

It's true that you can buy/sell such coins in alternative ways, but if your country explicitly prohibits it, you certainly won't dare try something like that. Just like you don't want anything related to gambling in your signature, right?