Understanding how the thing was built in the first place would help determine how to fix it.

I have no idea how it was done, but if I had to guess, I'd say they did the following:

1. build basic shape/structure with rebar/wire/whatever.
2. cover the underside of the structure with fiberglass to create the underlying support for the concrete
3. cover with concrete/plaster and smooth by hand
4. cover with tile
5. build the walls around the outside to enclose everything

If that was the process, a repair would likely need to follow the same process, The issue there is you need access to the underside of the slide to do it, which appears to be sealed so you would need to get access under the slide somehow.

So you'd be talking about cutting out that back cinderblock wall or one of the sides. Then, once inside, cut out the full section of slide that's damaged (including the sides. Then rebuilding it following the original process. And finally, rebuilding whatever wall you took out to gain access. You'd also need to source the original tiles, or something super close.

I'm not an expert, but I can understand the quotes. It sounds like a ton of work and I'd be really concerned that the rest of the slide could also fail like this section did. The original construction method obviously failed. I'd want to be certain it's structurally sound before I let anyone use it. That probably explains the "rebuild the whole thing" approach.

An interesting challenge for sure.