How would that help the Allams change the name? If fan approval is important to getting the FA to approve the name change, it is hardly going to be seen as anything other than blackmail. If fan approval is not important to getting FA approval, why bother at all with a ballot?
A ballot on name change would mean nothing to a new buyer, he would want to take over now, not wait until the FA got round to saying "no" again. If AA sells he would be selling for a profit (even if that profit is only the interest received on his loans). The kudos and prestige of having taken a club from the Championship into Europe in so few years is all he needs. It's almost the final piece in his jigsaw.