"First, in all programming helps you become a better programmer, just in the same way as playing the piano makes you a better piano player."
I think it's a good comparison. Programming contest would be a very specific part of piano playing, like playing scales super fast. It's useful, but still a very small part of what it takes to making music.
I agree that doing these challenges helps you play the scales super fast. But I think the important segue to acknowledge is that the fastest pianists don't necessarily make the "best" pianists in terms of the quality of the compositions they're able to churn out. I'm saying that being a super fast pianist is not a necessary and not a sufficient condition to become a great pianist. Does it help? Sure it does! It helps to move up and down the scales and play rachmaninov for the evening's entertainment effortlessly, but at the end, it becomes one of many ingredients required to actually "make" good music.
The question is, is there a really good balance that we could engage in? What part of lives are best spent practicing heavily (and perhaps "composing" lesser music) and what's the best indicator to transition into a part where you're not practicing as heavily, but you're composing more music.
Or for those more fond of sport analogies, practicing 3-pointers over and over again. It's a very small part of the whole game and you need to excel at all the other skills required to be a great player. But I disagree with the blanket statement of OP that it doesn't make you a better player.
I think it's a good comparison. Programming contest would be a very specific part of piano playing, like playing scales super fast. It's useful, but still a very small part of what it takes to making music.