My family was close friends with a family of 3 girls. the older 2 did a lot
of different things and stuck to them. But the youngest would take something
up, decide it was too much work and drop it a few months later. Eventually
the dad put his foot down and said (I think it was over playing the flute)
that she was going to continue (and practice) until he said, rather than
moving on as soon as it got at all hard.

I think there's a very subtle difference between allowing a child to
find the right instrument and keeping them at one for the sake of them
doing an instrument. I tried violin and piano, and pretty much had to
continue doing one, which turned out to be piano, I am glad my parents
did put that pressure on, because I've gained so much from it, but
equally, not having a great ear (though it's reasonable know, I think I
developed it from all the piano playing), violin was too subtle for me,
I also don't have great coordination between the two hands, so piano was
more challenging than some instruments might have been, so I might have
got more out of a wind instrument, but who knows, it was subtle on the
boundary between making me doing it and letting me try too many things.
My husbands parents in the interests of not doing that would only let
their kids try one instrument and unfortunately my husband chose trumpet
(or cornet, maybe) and possibly didn't have a good teacher or good
advice about mouthpieces or maybe was even out of the range of lip
shapes suitable for a small brass instrument, but it didn't work out and
the poor guy got no more music teaching, when he's actually quite
musical and is a good, but untaught singer. Neither set of parents
really knew anything about music, so I suppose the one good thing is
between us we now know a fair bit about how things can go wrong for
someone who is fairly musical and how to get the best out of a fairly
average child who enjoys it!

Cheers
Anne