I played the AI in fighting games way back when I was still in infant school and the Internet wasn't really a thing for playing them, but why would anyone want to do so today? Fighting games are one of the very few genres where playing an AI just doesn't work. In RTS's, you can still have a reasonable amount of fun messing with campaigns and skirmishes (you can spice things up by including campaign-only units, such as in Starcraft / SupCom), same for FPS's to an extent (the first thing I think about is UT2K4 because I played that a bunch before I managed to get a phone line installed). I can't really think of many ways to spice this up unlike these other two genres, maybe M.O.M. mode in Xrd, but I have never touched it, apparently you can just give yourself nutty abilities such as Pot Busters while playing Sol and so on.
In fact, I think Xrd did the whole single-player thing the best because it didn't interrupt the *cough* plot with an AI fight every 5 minutes. You just sit and watch the silly story until you get bored and do something else. In fact, I don't think I ever did a single character story in SF4 in its entire lifetime, I just watched the anime cut-scenes on YouTube. I did them in SFV just because you get FM and unlock the costume for purchase, and thank the lord they only take a few minutes each to blitz through.