I kinda want and not want it. Because you do tend to judge people on their voices not only on their game style.
One way it would be wonderful way to encourage team effort, making friends, etc. Because when you have a Trio or a Quadra team up, one or two people are left out of the loop, and people tend to forget to ping or tell them when they are ganking because of it. Those who team up generally blame the left over members for not being in the same loop, even if they end up in an undesirable role. This would be a wonderful way to eliminate that. There is a site but not everyone believes that links are innocent and not viruses, and don't trust them, and you can't blame them.
One way I do not want it, of course the raging, but generally Raging from what I noticed is downplayed when everyone is communicating vocally and accepting failures at times and realizing what they could have done. But there is sexism and racism sadly, and some voices are easier to determine races than others, and you can generally tell a woman's voice from a man, unless it's a kid that hasn't gone through puberty. Certain players could be toxic because of it. It would also be harder to prove someone was toxic in a vocal chat rather than in the text chat, unless Riot recorded all vocal conversations and allowed the Tribunal to overview them which could get time consuming.
I'm personally fine with a Separate Application such as Skype or Team Speak, but again, not everyone has them, or are willing to share their lovely voices, etc. I can see something like this being tested in PBE, maybe a choice of a vocal chat or not, but you would still hear your teammates talking, but this would have to see if it affected people's FPS or ping any as well. Time will tell.