I don't know anyone who uses CRT screens for their computers any more. I expect some do, but those of us who don't use CRT screens (i.e. those of us who use LCD or other flatscreen monitors) really have little need for screensavers.
Those old CRT monitors also used a lot of power and time to start up again after being turned off, so shutting the monitor down wasn’t the best idea, either. The solution was a simple program that kicked in after several minutes and ran some basic images across the screen to keep the phosphors from getting bored. Thus, the screensaver was born.
Yet many of us still use screensavers. I do. I love seeing a moving collage of photos taken at a huge family gathering a couple of years ago.
The only possible drawback is that screensavers use more electricity than a blank screen uses. But that is easily dealt with. On my laptop, I set the screensaver to show only briefly when I'm on battery power. Otherwise I have it going for quite some time if I'm not using the computer.