I haven't had this happen to me specifically, but I know it's happening out there-- players are blocking battlemasters by flooding around them, and hiding them inside other models, leaving them unclickable. We've heard about this before, and apparently it's a growing problem.
So Blizzard has come up with a fix-- in 2.4, says Tigole, all the battlemasters will be standing on platforms, which will be coded with collision, so player models can't invade them. It's not that big a change (imagine the auctioneers in Ironforge and Silvermoon), but it should make for a little different visual-- it'll be a crowded little pavilion where the battlemasters are in Shattrath.
Of course, that doesn't solve the problem of blocking NPCs, only of blocking battlemasters. But there are probably enough repairers and questgivers around at this point that there's no reason to put all the NPCs on pedestals just to keep them away from the maddening crowd.