Then Google could ship that dictionary to all (Chrome) browsers and update it once a month, and ship the same dictionary to anybody who wants to use it on the server side. Browsers can indicate which shared dictionaries they have preloaded and if there's overlap with which dictionaries the server has, the server can just choose one and use that to compress the stream (which seems kind of like ciphersuite negotiation). Compression should be faster and use way less memory if the sender can assume that the receiver already has the same dictionary, and if there's any problem, both sides can just fall back to on-the-fly compression with inlined dictionary like we've always done.
There are almost certainly different optimal dictionaries for different locales / countries, each of which could be calculated and distributed in the same way. Even if the 'wrong' dictionary gets used for a given request, it's (probably) not catastrophic.
I guess it might be possible for an attacker to indicate their client only has one dictionary and request pages that they know are disadvantageous for the server to have to compress with that dictionary. Even then, server-side heuristics can account for a lower-than-expected compression ratio and, again, fall back to on-the-fly dictionary calculation.
Web is more sensitive to latency than bandwidth, and upload is more restricted than download. So rsync hits all the worst spots, for the least gain. The data that diffs nicely, like HTML, is already tiny and compresses very well. The large files, like videos, don't diff well at all.
There is a way to make rsync-style differential download really quick to request: the client and server need to agree on diffing only from a specific shared dataset… like a dictionary! And you can replace hashes with smaller variable-length integers.