You make some good suggestions. All very interesting, but there is a bad side to this.
The bad part is that I don't want to design a player's character for him. Which is what happens if they just draw points off the Enemy quality and call it a day. I want them to be more invested in their character than just looking at a pile of points. If the player works with me and comes up with a good story, then, as I said earlier, I generally allow it. But the player has to put in the work to make his character interesting and engaging. I'm not doing it for them.
New players? Sure, I expect a bit of work. I also tell them to avoid certain things during character creation, and the Enemy quality is complex enough to distract them. I can see adding an enemy to that character later, after the player has gotten some real world experience under his belt, and even granting the BP for the quality post-creation. That, however, is something that new players get, and not more experienced players who are just not involved enough in their character's story.