OP, you haven't considered the timings. Places which cater to school groups are much more expensive mid week during term time because that's when they're in demand. You would pay a premium for outdoor activity centres mid week during the summer term. Like how places that cater to families shoot up in cost during the summer holidays.
With staffing, centres / organisations we have used offer different rates depending on how many of their staff you require. With parents attending, you'd need the absolute minimum centre staff. If you can only take minimal school staff (due to cover needed in school) you pay more for the centre staff to make up the ratios. A recent (admittedly expensive) school trip would have cost the 20 students £50 extra each if I weren't able to attend (in my half term without additional pay).
With charities, it is likely that the centre may have a special lower rate for them. Either because they can claim tax deductions or they can advertise how good they are for children with special needs (or both).
Rugby clubs (and similar) often have plenty of volunteers willing to go, and their places may be funded by the club rather than the kids going. And they often use club funds to help with the cost.
I agree with you that children shouldn't be left out if their parents can't afford it. But I also really don't like the idea of getting rid of school trips / music lessons etc entirely. Enrichment shouldn't only be for the kids whose parents can afford private school.
This is one of those things which is often discussed about London schools having a massive advantage. As it is the capital city, there are far more enrichment activities which can be done for free / minimal cost compared to those of us in other areas.