I totally agree. That's my first argument against the idea of the OP.
In these days you have out-of-the-box so many already working API clients and already so many public API End-points that it would be really, really hard to create some ( opinionated ) better way of doing this.
Libraries like Backbone and platforms like NodeJS ( and many more ) have this idea so deep that it becomes extremely easy to create an API front-end / back-end app with just a matter of a couple of files ( even lines ). This is becoming standard in other platforms as well.
I think the debate is long time shifted from "Is REST good for my app?" to "How to best follow RESTful principles in my app?"