I'm talking about public services. For private services I have no idea what they all do and, as importantly, what they are legally bound to do. I would hope that obviously they would have to provide at least 1 solution that doesn't rely on any third party, e.g at least provide the card reader with legal Belgian ID option (which seems to be what they offer you, so IMHO that's good enough), but I don't know.
ItsMe not running is pretty good in terms of privacy because their entire business model is, and correct me if I am wrong, to be an intermediary. I didn't check what data they share but I'd be pleasantly shocked if it was none.
The card reader might seem slightly inconvenient or outdated but there is no intermediary and it is, AFAICT, secure because it's based on well established cryptography.
PS: it's also fun because you can play with PAM and thus, I didn't try that, login or get su and sudo with your ID card.