I see no point. League isn't really set up to do things like achievements or rewards. Riot had put an 'Achievements' tab in the client a long time ago, and it just sat there unused for a long time. Got replaced by something actually useful (custom item sets tab).
And tracking things like that is effectively all it would do for you. You would just have to have Steam running, select League, and then it would open up the LoL launcher. I don't really see this as an improvement in any way. If they wanted to make it actually launch directly from Steam, they would have to make a lot of tech changes to the current system. That wouldn't be remotely worth the required time investment.