I see no reason why you can't have both an assassin faction and assassinations tailored to your character. In fact, I think the two systems work together. It's a bit like how in Oblivion, a lot of the Thieves' Guild quests were just "go out and steal whatever you want" rather than preset quests. In addition to scripted assassination missions, you join an assassin faction to have a support network, and the game will be able to use your superior to give you generated assassination missions.
True, but private assassins are not tolerated by the dark brotherhood. They'll kill the guy who gave you the contract and then they try to kill you.
It would be nice if you have both the option to join the brotherhood or be a rogue assassin and be marked for termination, just not at the same time.
Every time warm blood gushes over your hands the nightmother knows everything about it, so it will hurt my inner geek if they suddenly aren't able to know about it anymore, or don't care you make money behind their backs.