I have to take issue with your view that factoring quadratics is unimportant or overemphasized. Personally I think it's a fundamental skill that transfers well to, and aids in, other more advanced techniques in applied maths. The mental juggling you mention is a quite important skill if a student is to continue their study in maths. That said, your applet looks very useful for helping those students who might be struggling with it.
Perhaps one of the reasons students find difficulty with factoring is due to the point at which factoring is taught. In my view, there is a lot to be said for this sequence:
1. Parabolas in the real world;
2. Graphing quadratics;
3. Visually finding zeros;
4. Factoring, with the connection to zeros hopefully coming out easily;
5. The quadratic formula;
6. Completing the square, with (depending on the aptitude of the students) the derivation of the quadratic formula.
Speaking for myself, I didn't come across the factor-remainder theorem (formally, that is) until I was at university, while I learned quadratic factorisaton at around 14 yrs old. It's probably safe to say that I was "bludgeoned" with it, but it definitely didn't do me any harm....