Is there any security cards that just use NFC (with physical button, obviously)?

I think government issued cards are good contender for this. Perhaps it could even replicate certificate authority chain principles - certain cards could sign other cards and then can be invalidated if compromised.

My local id card is absolutely pathetic. I have no idea where to get a reader (although they are generic) and worst part is requirement to run Java applet in your browser - something that has been dead for over 10 years...