The good thing about the system as it stands is that the objective is very clear. You want to win. To do that you destroy the enemy nexus before they destroy yours. That is how you will get your LP, it is the same for everyone on the team. So you can make all team decisions towards that one goal. If you add a bunch of satellite objectives, than you really derail that goal of trying to win.
Say you are going to lose, well, better go do my mini-objectives so that I can soften my LP loss. This would happen tons. Lots of people currently give up games that are completely winnable with a little teamwork, these side objectives would make the "giving up" rate higher. We will just lose anyway b/c top gave first blood so imma just sit in fountain and spam my sight stone so I have plenty of wards placed...
This idea also puts even stricter restraints on what a player is allowed to do in game. This is your role, you had better do it this way! It can dissuade players from trying to be inventive, and that isn't really a good thing. (Whether you want someone "being inventive" in your ranked queue is another discussion that I'm not addressing here)
I would rather keep a clear goal of we all want to win instead of having that be a secondary objective to padding my own stats (I mean, you already see pro's padding their stats for fantasy LCS players, and they are kinda playing this game for keeps!)