Not the same. We all can walk or run or swing a bat, it's an even playing field. Some people are naturally faster than I am but I can develop other skills to compensate.
And actually, I don't idolize athletes as much as many people do.
We can all sing, too. Well, unless we are mute.
I understand where your argument comes from. Some people are good singers without any training or practice; they simply are born with good voices.
However, I think you may underestimate how much of a musician's talent is also something they are born with.
Yes, through practice just about anyone can learn to play an instrument, even if they don't have a natural aptitude for it. By the same token, even most of those without a natural talent for singing can learn to improve their singing voices. In either case, without the right genetics, I don't think a person is going to reach greatness.
I think your feelings may boil down to the fact that singing is more natural than playing an instrument (with the possible exception of drums). Singing is just something you do, from the time you are a small child. Good or bad at it, just about everyone sings. Far fewer play guitar, or piano, or violin, etc. Singing is the least....man-made of the bunch. I'm not coming up with the most appropriate phrasing, but hopefully you get the idea.