If persistent connections are patchy, then HTTP is no further ahead.
A sure-fire way to decrease latency is to send as little as possible.
An empty default browser HTTP request is likely to cost you around 500 bytes in headers, before you have added any headers or data. Contrast that with a binary command which can be 1 byte. And then multiply this by hundreds of requests. CPU cycles on mobile are not cheap. It makes no sense to parse 500 bytes (and then GC this later) when you don't have to.
Even on servers, parsing isn't cheap. Look at nginx code or other high-performance parsers. All sorts of little tricks to compare 4 or 8 bytes at a time to determine the verb and whatnot.
A sure-fire way to decrease latency is to send as little as possible.
An empty default browser HTTP request is likely to cost you around 500 bytes in headers, before you have added any headers or data. Contrast that with a binary command which can be 1 byte. And then multiply this by hundreds of requests. CPU cycles on mobile are not cheap. It makes no sense to parse 500 bytes (and then GC this later) when you don't have to.