As I understand it, you can access them for free with your own equipment, or rent the gear, or go with a guide. Most tourists are going to go with a guide at least the first time and probably rent gear afterwards. They might ask for donations for the maintenance, although generally I think that's paid from the equipment rental/tour income, subsidizing it for people going on their own.
$200 sounds about what you'd pay for a guided tour (gear included) in Switzerland.
Honestly, what real benefit does a guide bring to most reasonable people? I know, the stereotypical American will travel to Iceland with norhing but shorts, but those aside, most everything to learn/understand here can be explained in an 2-5 minute introduction of the equipment. I mean, both me and my brother managed without problems (under paternal guidance) starting around age 6 two decades ago. Nowadays, most seem to be super crowded in the high season (meaning well, you have to wait often on a route), but its always been a fun activity.
It's still unfamiliar terrain, and a guide will help you find the start of the route, will help you get through a difficult spot and can perform first aid if needed. So if you're not an experienced hiker and climber, going with a guide will make everything go smoother the first time.
$200 sounds about what you'd pay for a guided tour (gear included) in Switzerland.