You're also potentially opening yourself up to any apps/tools that are keeping an eye on your clipboard if you're copying and pasting. Auto-type might help with that, but I also wouldn't hold my breath for such a feature coming.
Compromising everything is easier, it means you have to change the password for everything and know it was compromised.
If only SOME stuff is compromised then you don't know what was compromised so you end up having to change everything anyway.
I mean, that's at least my approach. I'd rather know I needed to keep an eye on everything rather than some things. At least then I know I can take appropriate precautions.
Its a poor argument for choosing browser extensions over cut & paste because the circumstances where it has an advantage are incredibly specific.
I think the separation of concerns outweighs the KeepassXC<->Browser integration part.
If your computer is compromised (meaning occasional copy&paste is not secure) you have WAY more problems than only Keepass and phishing.