The Web services I've used tend not to be super complicated. A handful of api calls tend to be used.
There's also versioning, which is handled well with a good url structure.
Also, the schema problem is more of a JSON vs XML issue. I personally use JSON because it's simpler for flatter data graphs. I also use JSON schema btw. XML does have the advantage of xpath (or css selectors) too.
But even in the REST + XML case, the XML is simpler than the XML + SOAP case.
Which brings up Content-Type. Rest can serve pretty much any content type in a way that's readable by almost any web-enabled client. Not so with SOAP. You need to have more software.
Basically, I can add these features on an as needed basis. REST is easier to work with right now and I probably will not need all of the features of SOAP. That's the gist of why it's less popular now.