That's just the plain text (or whatever files), that's not the context the model is directly working with on the server, which is tokenized, embedded, vectorized and has attention run against those vectors. The local history is generally quite small, the context generally quite a bit larger. A text conversation of a few hundred kilobytes in plain text will be gigabytes in context.
To me it would certainly make sense if the protocol just said "append this text to context window id/sha256", in particular as the data is cached in tensor level in the provider side, so they need to first do that lookup anyway. So I would be surprised if they don't have that.
In addition, this protocol could make it more transparent to say "oh we cannot proceed as we dropped the this cache, are you sure you want to proceed and consume a whole lot of expensive uncached tokens?". Oh, maybe that's a reason not to do it..