Curse Voice and 3rd Party Programs

The point isn't the effect they could have on you. Sure, muting does stop you from hearing their rage, but it doesn't give them any less of a reason to stop being angry. It gives them another reason to find excuses as to why they're doing poorly and another person to blame for it.
It's not that people get banned for refusing to communicate. Getting banned isn't the problem. Something unnecessarily creating issues and divides within a team is much more problematic.
Yes, people are already raging with typing. But just as talking is easier to communicate, so too is it easier to rage with. Muting everyone else because they're raging completely defeats the purpose of the voice chat in the first place.

I don't play LoL but I saw some discussion over in the Dota 2 reddit and I thought I'd rather contribute here than there. The two are very similar games and I'd say that the communities are fairly similar too, at least when it comes to poor behavior and I got to say that ragers and flamers aren't that common in voice chat. I think I get flamed more often by people that type than by people who talk. Most of the times people won't even use either because pings and wheel chat commands (short sentences like "missing mid", "push", "I'm out" and stuff like that) are enough. Regardless, I think that having the option to use it (even if just to listen to others) is a whole lot better than having nothing at all. It's just up to the community to make good use of it and make it "ok" if you decide not to use it.

I've muted a whole lot of people (regardless of what method of communication they use) and it's not near the amount of people that are ok or friendly or cool or -something positive-. As much as I dislike flamers and ragers and whatnot I've also "met" cool players and I play every not so often with them so, no you're not gonna mute everyone and chances are you'll meet cool people too instead of only trolls, flamers, etc. I'm 100% sure that this isn't Dota 2 only, I'm certain there a whole lot of cool/friendly people that play LoL.

You're trying to say that the program is optional, yet at the same time saying that it will simplify the game and make it easier. I see those two as highly contradictory. If it's allowed, optional, and makes the game easier, why wouldn't it become mandatory?

It won't win you games. You can communicate as much as you want with your teammates but if you aren't skilled enough it won't make a difference. Skill alone gets you further than communication in Dota 2 and I'd assume it's the same there. I've never used voice chat and most people I play with don't use it either, yet we win more than we lose.

Although it's a team-oriented game, solo queue is reliant on the skills of the player. How much different is being carried by a friend in duo queue, and doing nothing but blindly listening to the commands of a smurf or a better player through voice chat? It lets people skate by on everyone else's coattails.

Unless mechanical skill is irrelevant there, which I doubt, it doesn't matter if you get Sun-Tzu to tell you what to do, it won't get people carried there as it doesn't get people carried in Dota 2. I once got a team mate who drafted for us and was giving us "awesome" instructions but we couldn't perform them for several reasons, one of them being our skill level.

And obviously there would be a rather large problem with shy/quieter players trying to contest the ideas of louder, more verbal players. A shyer platinum player could get outshined because some loud bronze rallies the entire team to their poor decisions.

That is indeed a problem. If it's a bad decision people will gladly point it out and plan something else, and if that fails the first person gets annoyed at you.
The thing is that it's better to have the option to say "nooo! D:" than watch them mess up as you type "don't do that, you're going to die/whatever".
I guess it's a matter of preference, but I think it's unfair to only point out the cons.

But the idea isn't just the problems it could create in gameplay. It's the idea that allowing these types of programs also allows for more complex and invasive programs. It's WoW syndrome. Take a look at some of the master yi and cassioepeia programs circling around. Allowing one allows another.

I agree with you, having something else keep track of timers for you takes out a lot of skill/knowledge that makes the game "deep" and fun. If I were a LoL player I wouldn't oppose voice chat at all because there's an example of a very similar game that uses it and it works fine but I'd definitely be against any sort of cooldown/timer tracker.

Also, in addition to the shyness thing, think about other effects voice chat with strangers could create. A guy with a feminine voice could get flamed for being gay, people could be attacked racially for having a distinct accent or voice...

You're completely right about that. I'd assume both communities react the same to "foreigners" or anyone with an accent and it truly sucks. I think it affects how much you can enjoy the game, even if you're not the one being flamed. I often tilt when pimentos start harassing someone because of their accent even if I know they're just trolling and baiting to start a stupid argument.