If anything I'd say REST is dramatically worse in this respect. There's no structure for nested queries (or anything except thing/:id really), so the only broadly compatible option is to pull every piece as a separate GET request.

Sure, you can use query params... but there's no implied support nor semantics, so one site will do one thing and another will do something from a completely different universe of architectural patterns, while a third will just have nothing, and there's no way to reconcile those in a consistent way.