I really want to get the speculation rolling on this because it's kind of a big deal. I don't know a lot of game designers/directors out there in the world of ARPGs that are available. I know there are the typical (somewhat silly) suggestions of Schaeffer and Brevik (or Brother Laz!) but those are not going to happen for obvious reasons.
I myself don't have much to offer here either as my industry knowledge is kind of limited. I will say that Cliffy B. is currently not working on anything. He's made some competent games and seems like someone who understands fun, and understands action games, (yes, yes, I know, D3 is also an RPG) but that's not really what the game needs right now. But I'm just throwing stuff out there. (Also, Cliffy B. Diablo 3 rhymes. An essentially element for any game director.)
How about... Yasumi Matsuno. lol okay, no. But he did make Vagrant Story, a type of ARPG, with a seriously convoluted item system. Like, breaking items down to hilts and bits of string to recreate something godly. Okay, I'll stop, that's as crazy as Brevik coming back. Dude loves numbers and stats though, seriously. His last RPG was basically just dice rolls. (Also: Final Fantasy Tactics!!!)
Honestly, I don't think we're going to get an ARPG expert here, because the genre is so small as is. So who will it be!?!
It's to late. A lot of things are set in stone. The most important being GAH and RMAH. This stifles any radical changes. Itemization can't be fixed without a worldwide wipe of all items. Story can't be fixed. Adding more features and systems will only increase amount of mess in PvP.
D3 is in a lot of ways like Windows Vista. Vista has been in development for a very long time, after widely acclaimed Win XP. It flopped and was quickly abandoned in favor of Win 7. The same holds true in D3 case. Not much can be done. There are to many major mistakes. We need D4, which will, of course, not happen. -_-
Director is not someone you just "be" it is something you "grow into" - similar to a company leader, the moment they are getting assigned from outside instead of promoting someone who is with the company for years already you notice the company starts to slow down. So obviously the best choice is someone unknown who has proven himself internally to be great at overseeing everything while keeping a clean head.
Fresh things should never be expected from the top-leaders of a project.. Freshness comes from having young personel, who are inexperienced (experience is actually more a blockade to being "fresh"), yet you don't want an inexperienced person running the show do you?
So older people should be promoted to do the management: fresh new persons hired to do the actual design.