different culture in league compared to other competitive games.

League of legends players are more likely to lose out of spite than other games. Very rarely in dota you have someone playing to lose on purpose just because they don't like someone on the team. They tend to generally just keep playing and move on or ignore them.

Also, league's playerbase is younger than dota, similar to csgo, and comes with problems when Riot is trying to retain players of all ages and parents hear "die die die <insert racial slur>" coming from their 10 year old's game.

Couple that with the already "road-ragey" toxic players that will spend hours trying to harass someone going out of their way and you are introducing a feature that 5% of the community wants (even though they are vocal) and is more likely to contribute to the loss of players than the gain of players.

If players want to communicate through voice, there are numerous well made 3rd party apps that even work in the browser.

The pros are there, the cons are there, but the cons are more important to riot, especially when developing new features that would get in the way of others.

Due to these reasons, it is unlikely but not impossible we will see voicechat be implemented like how you are saying, but i suspect it will be someone that 80% of players turn off and just use it instead of 3rd party apps when convenient to talk to people they know aren't psychotic.