The thing is, it feels like a sort of a waste when you finally found this awesome sound, but you can never get it again. It's just a one time deal. But I agree, sometimes one time deals are the best.
I think I understand this. You desire the spontaneity of improvisation combined with the traditional visual permanence of a score ? That little dilemma has concerned people for a long time. These days, using digital pianos, of course we do have the ability to print our improvisations. The trouble is that it produces the pitches accurately but, for all but the very simplest music, nothing else. We are still faced with the task of transforming the jumble of notes into a score which is communicable, and which, when interpreted, is likely to resemble the original idea. If you improvise in rhythms which are to a large extent notational the problem is considerably lessened. However, many (most of mine !) improvised rhythms are impossible to notate anywhere near satisfactorily and unambiguously.In short, most written compositions are to a great extent conceived for notation in the first place. Improvisation can still be used as a solution from which the crystals of a composition slowly emerge, possibly over a long time and many sessions. I think very many composers of piano music have worked in that way.But the most important consideration is the it not an "either/or" choice. You can compose and improvise and each can feed the other over a lifetime.
Improvising seems to me similar to walking on a dark forest path in the night. If you look straight forward on the path you don't see anything. If you look at the side, suddenly the path gets visible. You will again try to look straight ahead and the path will disappear. It happens often when you don't really focus intentionally on it, given that you have a desire to express yourself through music, through your own music, and given that you feel this music somewhere in yourself.
Recently I played at a birthday party and the person who introduced me said to everybody "He's an improviser"! Well, actually I felt completely blocked! Because to me it is not (yet) something that I just "can do". Fortunately I had not been asked to give an improvisation performance but to play from my compositions But really, that might just be me.
I think that is just a mental trick which can be learned over time, Wolfi. I used to be the same many years ago. The problem disappears once you realise that the reactions of people in the room do not matter and that you are essentially playing for yourself alone. Improvising with a view to impressing somebody is destructive because it will stop your flow. In any case, unlike when you perform a piece, the audience cannot possibly perceive "right" or "wrong" notes because these qualities do not exist in improvisation.