We did suspect that horse riding - my childhood hobby - probably didn't come out too badly in comparison. Yes, lessons much more expensive but kit apart from hat can be v cheap and bought massive until you grow into it no expectation that parents are going to help in any form, possibility of dumping child at stables for hours on end and child blissfully happy, no exams, can alternate lessons and hacks to keep costs down
Well, times have changed rather. You can't buy all the kit cheap and over-sized. Any decent RS will want kids in well fitting, suitable boots, a well fitting hat (yes, you can hire these, but standards and fit will vary in many establishments), and if jumping, a well fitting body protector. That's a lot of kit, and a lot of money, and you'd be mad to sacrifice fit, or quality, when it comes to PPE for a risk sport like riding.
As for exams, many kids will want to join PC (many RSs run branches) and do progressive exams. Many places simply will not allow you to "drop and run", other than on specified, paid, "own-a-pony" days because of insurance, which is already extortionate.
It's a brilliant hobby and a wonderful thing for kids to be involved it. But it's not a cheap option, and it is, ultimately, inaccessible for many (unless fortunate enough to be in hitting distance of one of the inner city accessibility programs).
As for spectator sports, most low to mid level competitions are free to enter (except BE, county level showing, racing etc), and there are more accessible "one horse" team sports like horseball and polocrosse. Horseball used to be played at Lee Valley in London, and is fast-paced and easy to follow as a spectator.