Why is it easy to compose piano music?

Because you have to start from where you are. This should be fairly easy; otherwise you have not started from where you are. A suggestion is to start writing piano pieces for beginners in a progressive order. The idea is that as the pieces get more complicated for the player they will also become more complicated for you to notate and compose and you will subsequently learn as you write.

How is composing beneficial for your piano playing?

One important reason is that your compositional endeavours will make you more and more aware of intrinsic musical subtleties in the music of other composers. When you start to think and feel like a composer you will also become a better performer as well. Performing is also a creative process similar to composing.

Compose and become a better sight reader

I remember an assignment I had many years ago writing music to my first musical. It made me aware of many notational problems I had not taken the time to solve for myself before. When I started to play my piano music again I was astonished when realizing it was much easier for me to sight read complicated piano sheet music. The reason for this I concluded must have been my concentrated effort to notate my own piano music. The process to play something with my fingers and and then try to notate the music on manuscript paper was so to speak a reversed sight reading exercise.

What about manuscript paper?

Notating sheet music is very cheap or very expensive. You can buy a more or less expensive notation program as I have done or you can write on paper or use both approaches. I suggest that you start writing on paper the way that composers have done for centuries. It is cheap and it is an effective exercise to use a pencil and writing the various sheet music symbols by hand. Very often I jot down musical ideas on ordinary white paper after drawing five lines by hand. It works fine if you can't find your manuscript paper. You can buy manuscript paper for sheet music or print out your favorite format on the site http://www.blanksheetmusic.net

It's of course up to you but, composing piano sheet music can become a natural part of your daily practice routine. Spending half an hour a day composing your own sheet music can help you increase your musical knowledge and help you become an even better musician and most important; it is fun!