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.

How much experience do you have playing other games with voice chat? I've played plenty of games with friends and strangers alike and voice chat does nothing to exacerbate these problems, beyond levels easily seen in type chat. Muting everyone does not defeat the purpose, it allows an option for constructive communication without making communication mandatory.. Not everyone will be worth talking to. That does not mean that no one is worth talking to.

I didn't say anything pertaining to why people will think CV will be mandatory because I didn't think it needed to be said. Look at the thousands of people that have already received CV keys and who are using it. Look at the thousands of people subscribing to twitch streamers specifically because they're giving CV keys to subs. If it exists and it makes the game easier, then people will flock to it. WoW is a prime example of that.
Hell, even maple is seeing it in droves. Hacking is commonplace, and the idea that buying NX items is mandatory for characters to do well is only a hop skip and a jump away from that; they're not much different.

You're significantly over estimating the number of people currently using CV. I've had it on since the beta began and only queued with two people that were using it. Both people were polite and focused on working together to win the game. In case you failed to notice, hacking existed in LoL before CV came along. There are already programs that automatically time buffs (even without vision) and even macros that do things like last hit or dodge skill shots. How exactly is CV creating a slippery slope when these programs already exist? IMHO hacking will not become as common place in LoL because the entire point of the game is competitive PvP. Sure there will always be a few people using autoaim or it's equivalent, but to the vast majority there's no point in winning by cheating.

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?

I think you're overestimating the advantage CV and voice chat in general provides. It makes timers slightly easier and communication faster. This is not the same as making the mechanical skill or the team strategies any easier.

There's a very large difference between principle and practice. Pings and voice chat are both means to the same end, but one offers unnecessary complexities.

How is talking more complicated? It could easily be argued that it's simplifying communication since almost anyone can talk faster and more clearly than they can type.

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.

DuoQs already use skype and other programs. Why should SoloQueuers in the same game be disadvantaged? Having someone make suggestions in voice chat will not improve your mechanical skill. It will not mean people will blindly follow one players directions. Even pros use skype programs and have designated shot callers who do exactly what you fear. Does Aphro and DoubleLift making shot calls mean everyone else is being carried? Hardly.

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.

If it turns in to a shouting match (a scenario that I find unlikely), how is that any different from spamming in game chat logs to hide someone else's?

Edit:
One of the posts I really liked on reddit talked about how it removes the human error from the game. Having it automate timers removes the ability for someone to make a mistake and write the wrong time or forget about the timer. Skill at its most basic level is the difference between players to make mistakes. Removing an aspect of that is putting it one step closer to botting.

How far off is simplifying the timers on objectives and buffs to simplifying the timers on enemy cooldowns and the like? They're the exact same thing. They're both gleaned through learning the game and getting the timings down.

I'm ignoring this since I don't really care if the timers are included.

Edit 2:
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...

I think people are getting overly sensitive about this kind of thing. It's not that I condone such actions, but the idea that a video game must somehow create a safezone in which this can't happen is impractical at best. I've seen no evidence that this kind of teasing/harassment has become a serious, widespread problem in other games. It's certainly not as bad as in a real life high school.

From your general arguments, I think I can distill the debate down to this:

Do the benefits of improved communication out weigh the potential for abuse?

In my experience, the benefits are common and the abuse is rare. The abuse is probably more impactful, but this is mitigated by infrequency and of course the optionality of the whole system.
I think it's worth it.