I'm not who you asked but I sent my daughter to a selective private school after her average state primary for (in part) this reason.
At 10/11 of course we don't necessarily know where our children's future interests will lie and we can't be sure how well they will do in the future. But mine was interested in languages at the time. There was no comprehensive in my local area (all are rated at least good) which offered more than one or two languages and at several of them you didn't even get to pick which one. At the school she ended up at, she could have taken any of six modern foreign languages and also Ancient Greek and Latin. She's studied German, French, Russian, Mandarin and Latin at different times and could also have chosen to study Italian, Spanish and Ancient Greek.
It was a given that she would do triple science (there isn't an option to do anything else).
She could have picked loads of creative subjects at GCSE had she wished to (she picked one, but I wanted her to have the choice of what she really liked rather than being constrained by option blocks). I don't see why a child who is that way inclined shouldn't do Art and Music and Drama if they want to and can cope with the workload. That isn't an option at any of our local comprehensives.
And she was able to choose subjects in full confidence that they would run whatever - like other things I have mentioned this is a funding issue. I know of kids at state schools who haven't been able to do the A Levels they wanted because there weren't enough children choosing that subject. But DD could do Russian with only four students in the class because the money was there to make it possible.
She did twelve GCSEs. This obviously would not suit everyone but actually it's great for children who are academically competent because during that time her preferences for subjects changed as they got a bit harder and more in depth. And the depth she was able to go to was absolutely enhanced because everyone was working at the same high level. Having more subjects for longer meant she was able to make a more informed choice when it came to A Levels.
DD has been able to choose what she wanted to study with very few limits. This would not have been the same in a state school (obviously not because they wouldn't like to but because they are limited by the ridiculous eBacc thing and by funding).
Private schools aren't all the same, any more than state schools are all the same, of course. But the one I picked was definitely able to offer more than any of our local good comprehensives.