The server side support seems like the wrong thing to base the protocol design on, but I admit that is probably just me showing my limited experience with very high traffic api's. I would think though that much of this could be alleviated by proper caching. As requests would naturally be finely granulated into individual resources, presumably that could be done efficiently.
The point of browser support is probably more pressing. I'm curious as to how big an issue that still is? Which browsers support it properly these days and which don't?
I wonder if it would be worth to build an api around the assumption of support for pipelining and then provide a fallback hack for those that lack support. E.g. something similar to the good old _method hidden-field hack for lack of http method support. I'm thinking something like an optional "batch request endpoint", that would tunnel through multiple requests, similar to what a pipeline would do. I believe Facebook is offering something similar in their api's.
In theory, things like pipelining allow you to never have to worry about compound documents. In practice, I don't know anyone who has gotten this to work well for browser clients and general-purpose frameworks when dealing with non-trivial numbers of documents.