Hi OP, we're probably a few more years down the line than previous PPs', but can concur with some of the negatives of competitive swimming...hours spent poolside, swimming hours before/post school, weekends taken etc.
My DD is now 13.5, came into competitive swimming later than most so was on catch up but has really closed the gap now and is still enjoying the sport. One of reasons is I think this is because she is still seeing progress over a short time, where some of her peers who were seen as child prodigies have plateaued, down to a mixture of lack of patience (body changes slows down progress) and the 13/15 attitude barrier. It really is a long time to spend in a pool if you don't love it.
is it really something worth doing that can lead to other opportunities
This is quite subjective, I can only talk from personal perspective, but it really helps my DD to organise herself across all things she does, and having a physical outlet helps her with her academics. Yes, there's lack of time to study, but what she does, she does it efficiently and still to a high standard. Also is very resilient (swimming has lots of knock backs), but has a group of friends outside her school life that helps through the fickle early secondary years. It does impact on other things she's had to give up now due to commitment to training (we're at 14 hours per week), but it's offset by being around people who get it. She's at peace from withdrawing from school sports squads, but if she chose to walk away from competitive swimming, there would be a recreational squad at her club with flexibility on sessions. But she's competitive - I think it would be all or nothing for her.
Lots of parents say when their children give up, what a waste. There will be potentially more things to gain that are not so easy to quantify but are character defining, therefore we'll have no regrets here when that day comes.
Re independence from 11/12 - absolutely encourage it. The less time you spend pool side/making other family members suffer, the better. There's a big uber-share thing at DD's club (but humble TfL works for us :) Take a deep breath also around other swim parents...they are HUGELY competitive, but if your child has a good attitude and appetite to improve through the peaks and troughs, this can often out-swim those with early innate ability that just burn out for one reason or another.
Good luck with your DD's swimming!