Sway bars are springs that reduce "sway" i.e. keep the chassis level-ish. More importantly they reduce weight transfer to the outside wheels maximize your tires patches while cornering. More tire patch means more traction, more traction means faster.
The way they work, is one side is moved (up/down) relative to the other side and the center bar acts like a torsion bar and because it wants to keep the legs aligned.
A simple sway bar at rest, no load. This is the shape it likes, because it's a spring.
Then you turn right and the cars weight shifts to the left side. The car leans left and causes the left side of the sway bar to move up. This is counter acted by the right side and the sway bar wanting to be flat.
Stiff sway bars mean less movement.
You could stiffen the coils springs and reduce body roll too, but you also impart more energy into the chassis with every bump and reduce the effectiveness of your dampers and makes for a choppy ride. On real cars sway bars can improve handling (or make them undrivable) without effecting the ride quality much, within reason. If I put a sway bar from a semi on a Huyndai, it will probably drive and ride like crap.
In the end it's one thing to help you tune your suspension.
If you want more understeer stiffen the front suspension. If you want more oversteer stiffen the rear suspension. If you take it off, it will change the way the car handles, over steer or under steer ultimately resulting in change in more weight transfer and and less traction.
The only application that I know that sway bars are not desired is in rock crawling because you want the axles to articulate be misaligned. In this case it allows more suspension travel and the tires to contact the surface in extreme terrain. i.e. more tire patch.
On my speed car I have the sway bars installed. They "should" help the car be more stable when I make corrections at high speed and I would gain nothing by removing them.
Better question is why do you want to take it off/ what will you gain?