Is it not impossible to preserve a complete looseness of the wrist in piano-playing because of the muscles that connect the forearm with the hand?

By no means. You should only see to it that you do not stiffen the wrist unconsciously, as most players do. The arm should be held so that the wrist is on a line with it, not bent, and by concentrated thinking you should endeavour to transfer the display of force to the finger-tips instead of holding the tension in your arm. For this produces fatigue, while the way I suggest will lead you to develop considerable force through the hand and fingers alone and leave the arm practically limp and loose. It takes months of study under closest attention, however, to acquire this looseness of the arm.