It also depends on what you want from improvisation. Are you trying to compose a piece or to cultivate your ability to merge with the music? In other words, is the important thing for you in this moment the piece of music produced, or the act of improvising?
They're different talents, and different moments, and at any given point one can't be committed to both, as you've beautifully said. So there is the matter of alternating one's practice. When you are walking through the woods with a divining rod in search of water -- if you are thirsty, the moment the rod begins to tremble you set it down and begin to dig. But if you are practicing your skills as a diviner, then you give yourself over to the trembling, you walk a bit further to see what your fingers will discover now...
One needs both sensitivity in life, and water.