This is likely to be true in general because of the way people learn music. Composition is rarely taught at a young age, but it's quite common for children to be taught to play. Many of the great classical composers come from musical families (and you have dynasties like the Bachs), and the children are introduced to playing at a young age.
Once they've demonstrated talent at playing, it's then likely that they will either start composing on their own or their instructors will start teaching them composition. They can create pieces that they perform themselves, and this will get them noticed as composers.
So while it may be possible for someone who isn't good at performing to write great music, the learning curve will be harder and it will be harder for them to get published. As a result, most of the well known, prolific composers will have taken the more usual route through performing.
As for why so many of them were great performers, rather than merely competent, I suspect it's because most of the composers who were extremely profligate and also considered "masters" whose work has stood the test of time were musical geniuses in general. Many of them could create, perform, conduct, and teach, all at expert levels. Some were musical prodigies -- Mozart picked up the clavier on his own at 3 years old by watching his sister take lessons, the next year he could play pieces faultlessly that father taught him, and by 5 he'd already composed some pieces of his own.