1) Using a single compression context for the whole stream means you have to keep that context active on the client and server while the connection is active. This may have a nontrivial memory cost, especially at high compression levels. (Don't set the compression window any larger than it needs to be!)

2) Using a single context also means that you can't decompress one frame without having read the whole stream that led up to that. This prevents some possible useful optimizations if you're "fanning out" messages to many recipients - if you're compressing each message individually, you can compress it once and send the same compressed message to every recipient.

We used a streaming compression format that was originally designed for IBM tape drives.

It was fast as hell and worked really well, and was gentle on CPU and it was easy to control memory usage.

In the early 2000s on a modest 2-proc AMD64 machine we ran out of fast Ethernet way before we felt CPU pressure.

We got hit by the SOAP mafia during Longhorn; we couldn’t convince the web services to adopt it; instead they made us enshittify our “2 bytes length, 2 bytes msgtype, structs-on-the-wire” speed demon with their XML crap.