It is much easier for me to answer this question in terms of its negative aspect, that is to say, to enumerate purposes which have little or nothing to do with why I play. As my main drive has always been creating music, composition and improvisation, I use the word "play" to mainly, but not exclusively, indicate these activities.
I do not play for a living.
I do not play to perform. If my music gives pleasure to somebody else it is good, but incidental and inessential.
I do not consciously create music for posterity.
I do not play to compete with people living or dead, even for private satisfaction.
Neither praise nor criticism matters much to me.
I was never forced to play or learn, but rather I tried to force other people to teach me, and had to be forced to stop playing.
Now to the difficult part.
It does make me feel good - guaranteed - always. My music has never given me a bad moment. However that in itself says little. After all, many things from love and sex to strawberries and cream, crackers and marmite, cups of tea, have done much the same thing. The trouble is that in attempting a justification one inevitably lapses into using those little words of religious philosophy which say everything and nothing and nobody is left any the wiser.
Let's try a different approach. In any life there exist timeless moments, holes in the fabric of mundane existence, through which we perceive something else. Huxley called it "suchness" or the "clear light", Elgar called it the "other place", Beethoven called it "approaching the divine". The desire to capture the invariant, and wholly beneficent quality of such moments in some permanent form, using the intransigent and unutterably clumsy materials of hands, piano, recording devices and paper and pen, lies close to the reason I play. In this connection, transience and timelessness are not mutually exclusive.
But then why embark upon this activity itself ? My attempt at answering your question amounts to an infinite regress, an asymptotic series of "whys", each an explanation of the previous. The whole thing is really impossible to explain in terms other than itself. A rose is a rose....
I suggest you read Aldous Huxley. He is the only author I have ever read who has come anywhere near to explaining why I play music, and he was much better at English than I am.
Topic: Why do you play?