It can be damaging when it becomes no longer about the child themselves.
I am one of 2.
My mother insisted on at least one activity every night. She hated the idea of down time or that we should not be doing something every minute of the day.
Most evenings would be at least one afterschool activity (some nights 2) plus homework plus 2 lots of music practice. Weekends would be activity after activity.
My sister loved it - as an adult she is constantly busy. Involved in running several of these clubs while working and having many clubs of her own to attend.
I hated every moment of it. I had no time or energy for homework so I didn't do it. My music suffered in the end as due to the other clubs I had no time to commit to the practice. I didn't enjoy most of the stuff I did. Even when I had glandular fever and was missing huge amounts of time off school I was still expected to attend.
After a sponsered stay awake one night at 10yo I was not allowed to miss my piano lesson followed by orchestra practice followed by something else the next day. I was too exhausted to participate.
By the time I was in my early teens I did (in a week) piano lesson, violin lesson, rugby training, swimming training, orchestra (3 different ones), choir (3 different ones), guides, 2 church youth groups.
The sport replaced the dancing (2 different types) I did while younger. I never got chance to socialise with my friends. By 15/16yo I refused to go home just so I wouldn't have to attend activities. I failed my a levels as was to burnt out, at 19 I dropped out of university. I couldn't face any more stuff.
What worked for one child didn't work for the other but my mum failed to do what was best for us. One was happy, one was miserable. It didn't matter how much I begged I wasn't allowed to give up. SO while was perfect for sis was terrible for me.