Here's a bit of truth - while I have a lot of alt warriors, I don't play them much once I get them to max level. I have my main, who raids, whose gear I keep up to date and who I play often, who I indulge my transmog jones on - and everyone else, once I get them to max level and maybe get them some Timeless Isle gear, I stop. My most recent 90 warrior, a draenei woman, I kept up for a month before I finally just stopped wanting to run dungeons on her. My tauren has seen even less play.
Why? Is it just that I already have the one warrior, so why play others? No. Because even if that were the case, it doesn't explain why my shaman and my DK are both sitting there, doing nothing. My shaman makes potions and flasks for me, and that's about it. My DK is literally gathering dust. So, why then? Why am I not playing my alts? I thought about it this week while considering what to do with yet another Timeless Isle piece I could send to my tauren, and then I realized that he's off on another server, with no gold to speak of, and in order to get that piece gemmed and enchanted properly I'd have to play him for an hour or two to make the gold to do it - and it hit me. I already maintain my main's gear - doing the same work on my alts just doesn't appeal to me.
Having to get all their gear gemmed, all the enchants (I always forget boot enchants until I realize I'm slower than everyone else) - even when you can afford it (which I can for my alts on my main's server) it's just tedious, especially when you find yourself improving gear frequently. What enchants do I put on my shaman's blue weapons? Do I go for the good enchants and then replace them in two days when I get an LFR drop?
Ultimately this is what has me thinking about Warlords of Draenor. Gear has been and always will be an impediment to playing an alt - you have to be willing to put in the work to acquire new gear and get them up to the same level as your main if you intend to use them in that fashion. But the removal of the variety of enchants and gems we have now will mean there's less impediment to alt-playing.
Another thing that really stymied alts for others (not for me personally) was the way reputation was gated at the beginning of the expansion. Having certain profession recipes on vendors with requirements of revered or exalted was bad enough, but having two of those reputations locked behind another reputation ended up frustrating folks who otherwise probably would have been leveling an alt instead of grinding Golden Lotus in order to unlock Shado-Pan and August Celestials. With Warlords being less focused on daily quests this, too, could be less of an issue. Of course, without knowing what the reputations are going to be in Warlords and how they'll be acquired it's too soon to call.
The change in raiding, with normal and heroic raiding equivalent to today's flex and normal (but with both being flex in size, so that you can bring from 10 to 25 on these raids) may also be a boon to playing alts, since there's less need to gatekeep who comes along on raids. The creation of mythic raids with a fixed 20 man size may benefit or hurt alt playing - I don't expect it to initially benefit alts, although it's possible that people with alts of several different classes may end up switching between them for specific fights like we saw in progression minded guilds back in Wrath. That doesn't really benefit the average alt-minded player.
Garrisons, at present, seem somewhat unfriendly to alts to me. As it stands, you'll have to level a new garrison per alt, which seems like a lot of work and if garrisons end up being as vital to character progression as things like dailies, enchants and such are now then I'm concerned that people who like playing their alts will instead be forced to use that time to get their garrisons going. On the other hand, with garrisons offering small profession related perks it may be that some players feel motivated to get each of their alts a nice garrison to work from. Time will tell on that one, and it's probably the biggest reason I'm uncertain about whether Warlords will be alt friendlier than Mists was.
Now, Mists made improvements over time - the commendation system meant that alts needed to work less to get to the reputation levels for recipes, for instance, and new reputations that debuted later had more fluid questing and fun ways to get to max. So in the end, we may be moving in the right direction, and we'll see what we get in the upcoming expansion. Perhaps my legion of warriors (and my shaman and DK) will get to do more in Warlords.