There are ages below which you are too young to play full-sized pianos, or play every interval an adult can play. That doesn't stop you playing it at all. What's more, your hands and fingers stretch. It isn't painful to play the piano.
The stuff about loudness is just rubbish. There is absolutely no need for hearing protection while playing the recorder (a very quiet instrument), the violin or the piano solo. You have no idea what you are talking about.
And I personally measured my recorders with an SPL meter and found them to reach over 100dB(A) at the ear (played indoors in an ordinary room with furniture but without acoustic treatment). The meter used does not have a traceable calibration but in all respects behaves as I would expect a correctly calibrated meter to behave. I have no reason to believe it is miscalibrated. Recorders are only quiet in the bass. The high notes require much higher air pressure and can be very loud. Perhaps you are fooled by the lack of distortion. I played without hearing protection at first, but I was disturbed by the prolonged discomfort this caused in my ears. I then recorded my playing and reproduced it with loudspeakers. I was shocked at how loud I had to turn the speakers up to reach a realistic level. I think it's easier to judge SPL from loudspeakers because they do have distortion which serves as a perceptual cue. Pure sounds can reach dangerous levels without sounding obviously loud. I also think the fact that I was playing the instrument myself and not just listening contributed to my misjudgement.
I once shocked my mom by clearly hearing what she whispered from across a quiet room. And not like a room in a home, this room was about the width of a house. I think people massively underestimate how sensitive hearing can be for some people.
I was briefly made to play violin as a child, and I definitely hated it (fortunately my parents recognized this and didn't push too hard). The reason is in retrospect obvious: violins are loud and piercing and played close to the ear. Nobody considered hearing protection back then. I learned recorder as an adult and the loud notes can exceed 100dB(A) measured at the ear (both alto and soprano recorders, and recorders have very limited dynamics). Violins seem to be at least as loud. I would hate to play without hearing protection no matter how skilled I become.
Even in instruments where you can more easily play softly like a piano, the design for loudness can cause suffering. Pianos are much bigger than they need to be now that we have amplification, with correspondingly wide and finger-straining keys. Steel string guitars are louder than nylon but hurt more to play (and even nylon can hurt depending on your individual hand size and shape). I expect there are many children suffering hand/finger pain from being forced to play various instruments and genuinely hating it regardless of their skill level.
When a child hates something, there's often a good reason for it that isn't obvious and that they don't have the communication skills to explain.