Mainly, it provides a consistent model for handling the notion of a "field". Non-RDF apis typically return fielded JSON or XML, the structure of which is only specified within the documentation. In order to integrate two services not originally designed to inter-operate, you have to write lots of custom glue code.
RDF is at least amenable to writing generic "rules" to govern field mapping and inference, rather than one-off glue code (which usually ends up being a hacky script). So sure, if you're integrating one service, a hacky script is probably easier. But if you want a coherent system for integrating large numbers of services not originally designed to inter-operate, RDF makes things a lot easier.
So there's some benefit, even if it isn't as dramatic as its proponents claim.
Plus, there's the fact that while strong AI isn't yet on the horizon, RDF is a lot easier for weak AI (inference engines, data mining, etc) to ingest, and weak AI is getting better all the time.
Actually, one of the biggest problems with RDF, to my mind, is that it's structure makes it very difficult to get good performance with truly large numbers of subjects and attributes - and unfortunately that's just the area where it'd be most useful.