If arenas gave no gear, would people do them?

Yes and no, somewhere in between known as "a lot less."

In a way arenas did stop giving gear. More ratings meant that people couldn't lose their way to epics and as a result arena play went way down. Naxx gives better gear, faster.

People aren't doing arenas as much now that they don't give gear. This isn't really the fault of arenas.

I started a team today. We're not in much PvP gear, we've not done much PvP in a long time, neither of us have proper PvP specs. We got our asses handed to us a few times before the system realized we should be down in the noob section. We're at some sad low rating. But, weird thing is, it was fun. I'm actually looking forward to playing more games. We've only done 10, or maybe 11 so far, and then we did WG and BGs for some honor. I want to play more though.

Arenas might be horribly unbalanced. They might be gimmicky. They might be artificially restricted PvP in a small box. But they can be fun. The problem is that we've all learned to chase gear. What gives us the best gear in the least time? Go there! That's the thought process.

I think I figured out why I'm enjoying arenas again. They're offering something that I'm not getting from raiding: learning and advancement. As I get better, I actually see progress, I get somewhere. In raids, my individual ability is diluted by 25 people. If I screw up, so what? Odds are someone else would have as well. If I do great, someone else screwing up still ruins it.

Arenas are more conducive to learning. Early on when you're terrible, you lose a lot, but what do you actually lose? Rating? You can't go below zero and until you've won a bit, you don't seem to lose rating anyway. Repairs? Nope. Time? Instantly requeue and you're back in much faster than a corpse run. Arenas encourage learning with almost non-existent penalties in the learning stage. In contrast raids do all their punishing while you learn, then once you get it: easy street.

I've learned some useful bits. While it is tempting to stay close to my warrior partner while healing, don't do it with DKs around or it's just asking for pestilence. I've learned to love 20 second HoJ.

One of our wins was against a druid-DK team (that's where I learned to spread out) and I saw the druid wasn't topped off. He wanted some range to get MS off and heal up, so he started casting roots on my partner. HoJ locked out his nature tree, my partner charged in and started doing painful things. Just to be sure I threw up an arcane torrent when I thought the interrupt string was wearing off.

Another win was against a holy paladin-DK team. We were slowly losing, with me losing mana much faster. But then the DK dropped a bit more than he should have been allowed to. The paladin saw the problem and started up a holy light. Interrupt, DK died, paladin bubbled, noticed what happened, and left the match.

There aren't really moments like that in raids. Arenas are still stupid and terrible, but I think I might enjoy their stupid terribleness. :P

[edit] I forgot to add, read this post by Tobold.