Is it good to cover completely a room with sound absorbing materials?

No, most people believe that just by using traditional sound absorbing materials (typically the polyurethane or melamine sponges, but also the classic and most economic egg crates) the room will sound good.
Unfortunately it is not like that: these materials work well just at mid-high frequencies (from 500 Hz up), but they do very little at lower ones (from about F4 on the piano board downwards).
It is common to exaggerate using them in rehearsal rooms and in studios and this does more bad than good to internal acoustics. The result is always a ‘dead’ and ‘deaf’ room, it creates typically an unpleasant feeling to people staying inside it (dangerous thing for artist creativity) and it never solves the room’s problems at low frequencies (generally defined as a ‘boominess’).
To ameliorate any room it is best to study its characteristics, use specific materials in the right positions, as the science of Room Acoustics teaches.
A simple advice is to start by installing the above materials only on the 50% of the walls and ceiling surfaces, the lower frequencies can be tamed initially by using cylindrical traps.

Una sala prove con troppo piramidale
Example of wrong treatment.