Sometimes they make you explore music that you would not otherwise have chosen. I'd have played list A (Baroque) pieces almost exclusively out of preference, but learned to like some other things.
It also makes you do some of the technical requirements more seriously than you might do without exams. I didn't do exam sort of curriculum on one instrument, and although I did some work on the scales and arpeggios, I didn't do as much as I ought to have, in all the weird variations, double stopped, various positions, etc etc. and I really notice that now as an adult still trying to play along in an amateur orchestra.
It can make you polish pieces to perfection in a way that you don't when you are just learning them for yourself - you think you have a piece learned well, and move on to something new. But it's a slightly different level of polish for an exam.
And performance experience - I rarely did the actual exams, though followed roughly the syllabus, and I kind of wish I had, as I'm still so terrified of public performance.
And it can give you the discipline to have something to keep practising for, if you are the sort of child that enjoys music and wants to be able to do it, but can need some goals.
Definitely not essential, and no need to do them if a child doesn't want to. Also no need to stick ONLY to three pieces and scales etc; much better to do a wide variety of pieces, and then do an exam when ready.
The advantages can be gained by other similar things - festivals or concerts, for example, or chances for improv, or whatever given lots of performance experience, and if the child has wide tastes already and lots of discipline to work on technique, and enjoy practising, without specific goals or deadlines, then exams might not provide any further advantages in that sense. But for some children, they can be helpful as part of music education. Just not the be-all-and-end-all.