What is the usefulness of a screensaver on a computer using a LCD monitor?
- Information (rarely IME)
- To prevent you discovering that the brave new modern world (LCD) is
kinda like the bad old steam-powered world (CRT) in some respects.
If entertainment isn't a use, millions of people have no use for their TVs.
Laptops and modern computers almost all uses LCD display now and, AFAIK, they are not affected by this effect.
The little liquid crystals that twist (literally) to move the light around eventually find themselves liking a particular orientation, and tend to stay that way for a bit after they've been requested to do something else. In other words, they act like a tired old man: Capable of moving quickly, but simply unable to do so after being in one position for a long time.
Plasma displays are highly susceptible to burn-in, while LCD-type displays are generally less so. Because of the more rapid luminance degradation of current organic compounds used in OLED-type displays, OLED is even more susceptible to burn-in than plasma. In addition, the wide variation in luminance degradation with OLED  will cause noticeable color drift over time (where one of the red-green-blue colors becomes more prominent).
In the case of LCDs, the mechanics of burn-in are different than plasma and OLED, which develop burn-in from luminance degradation of the light-emitting pixels. For LCDs, burn-in develops in some cases because pixels permanently lose their ability to return to their relaxed state after a continued static usage profile. In more typical usage profiles this image persistence in LCD is only transient.
So, should I completely deactivate this feature and use power management instead
In order to save yourself, your equipment and your planet, you should probably turn everything off and unplug it all when not using it.
or I am wrong?
Not much IMHO, despite the above.