I don’t think it magically just gives you confidence. So there’ll always be those it doesn’t help.
But... the attitude and opportunities are better for building confidence, so I think it helps those where it could go either way to become more confident.
One example, netball tournament, my child’s state primary vs nearby friend’s private primary.
State: have a netball club that runs after school, and has run 2 half terms of 6 this year. Not everyone can make that day. Run once by a TA who played at a high level. Then run by teacher who just had an interest - and didn’t know the rules until she took over. They have one (just one!) broken basketball hoop, and part of the court is missing because there’s a storage shed on it. They wear school PE kit and have no bibs. Nobody outside of club knows who is on the team.
Private: they have netball as regular PE, every week, all year. The coach is a former England player. They have 4 beautiful courts with proper nets. It’s a source of pride to be selected for the team - there are professional team photos up. They have a lovely sports uniform and their own co-ordinated bibs.
So - local tournament, they brought 2 teams, looked fab, and came first and second. We brought one and had a great time, but did badly.
Which kids went home feeling confident?
I know it’s all anecdotal. But in my own children confidence very obviously builds when they do well at things. Private school often gives you more chances to be good at something - either more options, or just a better chance at the same options.
None of that example increases the confidence of the kid with social anxiety who can’t do sport. But for the averagely confident and sporty kid in the class... I think it does.