Going from Level 1 to Level 30 takes a lot of time. Accumulating enough of your favorite champions to play ranked takes time. Saving up for all the runes takes time. Making a new account is possible, but it's a new account. No runes, no masteries, no champions, no skins, no friends list.
That would be why permabans exist. If toxic players will not reform, then they are given the largest penalty in a F2P game. A reset.
As to why are bans given out when an ignore button exists, or why shouldn't there be a mute process? Because the actions requiring muting are wrong. Insulting teammates doesn't mean "Oh, just silence this guy and everything is fine!" It means "This guy doesn't cooperate with his team in words, if we silence him he will probably stop cooperating with his team in actions. We don't want trolling, so it's time to remind him that he's out of line."