Ehhhhh I disagree with OP, the exact thing already happens today with discord, skype, teamspeak, etcc. I use discord in pretty much every match, and every match that i have a queue partner. Voice chat is already optional for league, just through third party hosting. Adding it to the client could help increase game performance by reducing the amount of programs you need to communicate with your 5 man short of spamming pings and wasting time typing in team chat.
Pros
More streamlined communication.
Lighter networking demand.
Everyone has access to the same exact means of voice chat. (Opposed to me using discord, and my top laner using skype.)
Cons
It's WAY harder to regulate voice chat. How do you expect riot to hand out bans to people who are offensive in voice chat without actually listening to the recording? (I mean really guys, there's tons of room for abuse here.)
People will tilt much easier, rage quit.
I will have to hear how every 13 year old has had sexual relations with my mother.
As long as there is a simple means to mute someone I think it COULD work, but Riot needs to be careful here. This is a feature that you should be careful adding to a game where matches can last upwards of 40 minutes.