Isn't that's the core idea of blockchain games? For all transactions to be recorded on-chain

Well, yes I did think so. But there are some CCGs that are having good success (like Splinterlands and Gods Unchained) by just trading the cards as NFTs on-chain but the actual games are played off-chain. I'm not convinced the current blockchains have good enough performance to have complicated game mechanics calculated and recorded on-chain at this stage.

Hopefully this will change at some point but for now I think on-chain games have a performance liability and it sounds like you have some first hand experience of that.