That's the most obvious problem: You risk losing the very things you need to escape safely. A lot of cars need keys to, well, be cars, and when you're using keys for melee tactics, there's a great chance you're going to drop them. If you're walking home and those are your house keys, well, now you've locked yourself out of your own house.
Keys are also just not great weapons. Keeping them between your fingers makes for a really weird angle from which to try to stab anyone, besides the fact that you could seriously injure your own fingers in the process. Go to the supermarket and try to stab some produce with your car keys. You'll see how much it hurts, and also get to meet the manager!
Now, there's one part of this that's correct, in my experience: The eyes are a great target. Just about any self-defense instructor will tell you to hit the eyes, jab the eyes, jam your fingers into the eyes, scratch the eyes, yell insults at the eyes, or if you want to do a lot of damage, dig your thumbs or fingers in there and gouge. (Fun gouging tip for the kids: Start in the center and push out.) Not only do ten fingers beat three keys, but they'll also help you collect some handy DNA under your nails to give to police.