Their purpose differs between hydraulic and mechanical brakes.
On these cantilever brakes, the purpose is simply to adjust the rest position of the brake. If you have the screw fully wound out, you should not feel any difference if you remove them.
BUT there is be a real difference in properly bled hydraulic disc brakes:
Here, it is used is to adjust the point at which the brake actually starts to grip to adapt the brake to your hand size. On hydraulic brakes, this is the only way to do that (in contrast, you can e.g. adjust the cable length on cantilever brakes). If an adjustment screws exists, it is most often an integral part of the lever that pushes on the cylinder and cannot be removed. (Especially lower-end brakes do not necessarily have them.)
Depending on your hand size, it can be really uncomfortable if they grip too early. For example, I rode some trails with the brake (BR-M486) gripping too early. To keep my fingers on the brake meant a hand position that got really tiring after some bumpy sections. Then I adjusted the screw so that I could keep the lever close to the handlebar in a rest position and my hands never got tired from that again. (Of course, a similar thing probably goes for the brake point being too close to the handlebar.)