Consoles are easier in some ways, but they definitely have their share of issues as well. More expensive and time consuming to update on is one (patches), they don't run nearly as good as a functional PC is another. Fighting games take very little resources compared to other genres so running it wont' be a problem. You'll only be using one computer on FG's live most likely anyways.
Emulating won't be an issue if we're talking about modern games. Lag isn't an issue if you're playing live, lag online is an issue on consoles as well, and even worse (especially certain games where one console has an inherent lag time compared to another, ala SF4), with PC's this isn't a problem unless a person is running an ancient toaster. People love to talk about arcade quality. Arcades are really just computers in a giant cabinet, so it can be done outside of that.
For computer parties you're really better of simply using a laptop. I think of the issue comes from the fact that most people just don't care to learn how to use a PC (the fighting game community tends to be younger and also not as computer savvy and don't want/can't spend money on a gaming computer, even though it's cheaper in the long run), and it's not "mainstream" for fighting games. Consoles are just plug in and go. You can plug in a PC and use it too and with the cost of consoles going up with more expensive games, they are often just watered down PC's. PC's also have the advantage of accepting any controller and most are simply plug in and play.
I'm glad that more and more fighters are finding their way to the PC because I find myself gaming on it almost exclusively (between my desktop and laptop). It's already on, it's fast, the games are cheap, and you get some pretty neat mods and fan projects too. I'm just waiting for 3d fighters to find their way there.
For the foreseeable future, you will see gaming on consoles. Though with smartphones and portable games becoming more mainstream, I expect to see a decline in console buying when you could just get a PC at that point.
One more thing to factor is that gaming events are often sponsored by consoles, which is why you see their presence there. If a computer company was the main sponsor you'd certainly see more PC's.