I have often encountered musicians, both pupils and peers, who are intimidated by the idea of improvising music.
Of course it is quite natural to be intimidated or apprehensive of something you don’t understand. When I first heard Bill Evans play and improvise I was blown away but equally left somewhat confused as to what I had just heard. Obviously this is a very extreme case as Bill was one of the most proficient pianists of the last century and a total master of his art. It does surprise me, however, when I meet very experienced musicians who are quite defeatist about their ability to improvise.
Having learnt a number of instruments and languages myself, I fully understand the apprehension that comes with the early stages of learning. In the case of improvising it is not a language you are learning, you are simply telling a story in that language. Therefore if you know a few scales and few chords, then you are ready to tell a story.
I find the best way to approach improvising is over a very simple chord progression, with a very simple or repetitive melody. Blues tunes are often good for this reason and these are normally the first one would encounter in an ABRSM jazz book. Once one has learnt the piece, either by ear or reading, then they are ready to improvise. In its simplest form this could involve missing some of the notes out of the melody line, or alternatively adding some in. The next stop would be to start swapping notes of the melody around, probably just neighbour notes so it doesn’t get too confusing. Then lastly, changing the position of some of the chords and before you know it you are improvising!
I believe that anyone of any age can achieve this and start playing the piano and enjoying music, without being confined to hours of formal scales or exercises.