Piano has assorted benefits, sure. But I'm not convinced that it's worth making a major investment into unless you're focused on being a professional musician.
To this I would add: if you want to be a good musician, generally, learning piano is very helpful. You'll absorb a lot of music theory (harmony) by osmosis. I found that quite helpful in my music theory and ear training courses in college. Beyond that, it's harmonically richer and more fun to play alone than a single line melody instrument, IMHO. (I say that as a former flutist who still plays the piano.)
