All *A airlines gives their *G members physical cards. UA is the exception where you have to ask for one. I think they are being cheap really by not mailing it without having to ask for it.
A lot of lounges big and small card you. SQ SKL lounges do it frequently. Many *A airlines ask for it at check in too.
All travellers should carry it... if not on themselves in their check-in at least. Just like they would their PP or other lounge access cards.