Remember how people always complain "X" champion gets nerfed because of Pro play?
Well, Voice chat would fix that issue, or at least make the discrepancy between Pro and Pubs less noticeable.
The fact is, certain champions require a lot more communication to unfold their true potential, communication that would be provided through Voice chat yet people seem extremely opposed to the mere notion of having that option.
Just think about it; Shen would finally be a good pick in soloQ once again.
Especially champions that bring team utility or need good communication would finally start to be more solid options.
Hell, my boy Mordekaiser doesn't really work with a random support bot lane as he needs to manage CD's, all ins and overall just needs more coordination with his support.
So I can't really see why anyone would even oppose voice chat other than "OMG MLG13Year olds would flame me over MIC!!"