The 3DS is different, it's using a lenticular screen so your eyes actually see different images! The eye tracking allows it to work even if the position of your eyes changes (ie because you moved your head).
Presumably developers could have combined this with parallax head tracking for an even stronger effect when you move your head (or the console), but as far as I know no one did.
Do you mean combining the eye tracking with using a lenticular screen? What would do you think the use cases would/could be?
Well, there are two different ways (among others) that your brain detects depth:
1. Each eye sees the object from a different angle.
2. Both eyes see the object from a different angle when the object is moved relative to your head.
The 3DS does only #1. TFA does only #2. Presumably if you did both, you could get a much stronger effect.
I think the New 3DS had the hardware to do both in theory, but it probably would have made development and backwards compatibility overly complicated!