If you do music you have lessons outside school, yes. But there's also a natural system to work your way up, you can do grade exams, join an orchestra, or work to join a county or national level orchestra, and the better you do the higher level tuition you will be offered. And schools accept and expect that music students will be learning outside school. They aren't expected to spend 5 lessons a week playing grade 3 pieces.
Kids who are strong in sports will be in school teams, which are usually coached well beyond the level of the class. And there is a similar out of school system to follow through. They aren't expected to limit their running speed or not try to score goals in lessons.
Kids who are strong in English can use the same essay prompt to produce a far higher level of work. And yes they may well read more.
I'm sure strong maths and science kids will be reading around out of school, I would certainly expect that in any subject, but that isn't a substitute for teaching appropriately in school.
If there were a lot more open questions asked in maths lessons then it would be much better - and it's great if some schools do that. I haven't seen any so far with DS at all. There tend not to be as they are teaching to exams and tests which are stuffed full of closed questions. Again, unlike in other subjects.
As far as I'm aware, the high level outside school system for maths is UKMT. Which, again to the best of my knowledge, can only be got into via school.
And then there's the fact that schools appear to strongly disapprove of parents teaching them maths out of school. "Don't push them ahead with the syllabus, it'll just make them bored in lessons." It's not hard to see why parents think maths should be left to school, schools keep telling that to us.