The day when the next leader dies is already set.
Metzen would sure have fun to triple his work just to make a vote possible (and throw 2 developed paths away again). Not to speak of how it would delay the content-team.
If they actually gave a few plausible options to choose from there wouldn't be anything stupid about it. It'll stop people choosing a dumb option just because it's funny.
There's most likely already been tons of story written out that includes whoever Blizzard has already chosen to be warchief. Even if they let the community decide, they'd most likely have to completely change around a lot of next expansion's story and details.
What if they've already gotten enough writing done for it (you know, far enough that it's already into the next expansion) that player choice might conflict with what they've already got going. (Only the South Park guys can work that fast.. lol)