I actually really like this idea.
Perhaps, your prestige level versus other schools prestige levels. If you're a 5-star team, you can go play an away game at a 1 or 2 star team whenever you want. If you want to play other 5-star teams, you pretty much have to do home-and-home series, or negotiate a neutral site (and allow us to start scheduling neutral site games). Or if you're a 3-star team, you have to go on the road to a 5-star team, or maybe get a 2-for-1 or 3-for-1.
This will bring a level of realism to the game. We can also lock in long term series with teams, etc.
Why? Teams don't have this power. Conferences make the schedule.