How come voice chat isn't integrated into LoL??

Because it would be one of the most highly toxic experiences ever.

because nobody wants to hear 13 year olds screaming, girls being superficial, trolls spamming and people talking in some indian language.

Because the people who play league are the League of Legends Community. And the thing about the league of legends community is..

I just find it as an inconvenience, like everyone talks about the trolls and the 13 year olds but that doesn't stop call of duty from using voice chat lmfao and this game requires way more communication than that game. your pretty much forced to download a program like curse, teamspeak and Skype. maybe that's part of the plan though, give no voice chat to provide business to those companies

to avoid trolls I guess

There are no mobas out there that have an in-game voice chat... all of them use text chat, pings, other in game commands to communicate. If people want communication they have their options outside of it, Riot doesn't have to provide every little aspect.

Because of people like Spazie and Keyori. Not because they're bad people. But because of their reactions in game.

Play a game of Call of Duty online.

Riot made their choice.

It's extremely weird to be honest. Playing with randoms would be 10x better but also it would be harder to ignore. When people type cancer into chat, you can just look away. With voice chat, you'd have to stop playing and go out of your way to click a mute button that would be somewhere on screen.

Also harder to moderate. Chat logs can be saved and reviewed if someone is reported for saying something bad. In a voice chat, if someone wants to call you "N**" over and over and it's blasting on your speakers.. it's just harder to review and moderate even if all voice logs are saved.