You won't see it. I know what you're talking about because I did the same thing with a CR-V.
The Mazda's suspension is probably the most well-thought-out part of the vehicle. It's much more complicated than a lot of vehicles in the class. LOOK for the rear swaybar, you'll notice that it doesn't look like others.
Corksport was talking about a full-body brace for a while there; I don't know how that turned out.
I have been looking unsuccessfully for over a year for aftermarket bars.
I changed the rear bushings (22 mm) to urethane and that helped the handling a bit and was easy and cheap. Haven't done the fronts as they involve removing some sub-frame pieces and the bushings are unusually tall/high.