Arena NEEDS a match history that at minimum records matches played, opponents, and wins/losses. I've searched for other threads about this, replied, upvoted, and am now posting my own suggestion.
I just played an amazing match, where the opponent made a play just to point out something that I'd missed before beating them. I want to send a friend request to them to say "that was awesome, thanks!", and maybe play them again - but there's no way for me to find their full ID#.