I think it's plain old stage fright and shyness.

I think singing is a very personal thing as it is a sound you produce yourself and is therefore more 'of you' than music played on an instrument.

An instrument can often be a distraction from the musician in their mind.

An example is Hendrix who was an invalid without his crutch/guitar, but who expressed himself beautifully through it. He hated his siinging voice and considered it seriously sub par despite being a consummate performer and in my opinion having a superb and distinctive vocal style.

So when a modest kid gets up with their instrument, they can filter any attention they are getting through it and hide a bit better.

When you're singing you don't get any protection in that sense. You have to sit/stand up, clear your throat and give it your all or not bother.

And that can be a struggle for most people as most people are modest.

That is why stage schools and workshops are useful for kids since they help to remove those inhibitions and barriers.