Higher speed which you take a certain turn at doesn't translate to better handling. Of course, it's all up to each one of you.
But damper and spring are pure physics, plain and simple. If you compress a spring, without damper, the spring will oscilate indefinitely when you release it. The stiffer the spring, the stronger its forces to continue oscilate.
Damper's function is to damp the spring's force to oscilate. In short, damper's function is to control the spring's forces. The damper will also have to work harder to control stiffer spring's forces.
Now take a look at your stock shocks/dampers. They are designed with lighter stock spring rates. They work very well with the stock springs, because they were engineered together.
Now you replace the springs with lowering springs which have higher to much higher spring rates. What happens with the dampers? They can no longer do a good job at damping your spring's forces. The higher the spring rate, the worse the overall suspension performance if you keep the stock shocks.
If you have mild lowering springs, like Prokits, HTechs, H&R Sports, stock shocks might still be acceptable.
But if you run H&R or Neuspeed Race, Tein STech, Eibach Sportline, or the like, your suspension actually performs worse than at stock height. This is why the spring manufacturers always recommend aftermarket shocks for these springs.
Most shocks also work optimally at a certain length range. If you lower your car so much, the stock shocks are out of this optimal range. It means, they won't perform as well as when they're at stock length.
stupidaznmunkey, you feel that your car handles better than stock, because you are riding on your bumpstops. When you take a corner, your suspension is at full compression and has nowhere else to go. That's why you feel your car is very firm and well planted. The real test is when you hit a bump mid corner. I guarantee you, at 90 mph, your car will snap into oversteer and lose composure. Don't ask me how I know.
Again, it's all up to you, but springs and shocks work according to the laws of physics and there's no way to cheat it.