You can't tell user-agents "the cookie I set must be valid for example.org and websocket.example.org but no others" (the example is crude and non-scalable, real-world semantics of this must be different), which leads to all sort of problems. Heavier static media requests, mixed cookie state if you use staging.example.org for pre-production environment, inability to provide third parties subdomains for their UGC, etc etc. All can be solved but not really convenient.

Would there be a way to have good control over cookie scoping, a lot of hacks would be gone and www/non-www distinction would be purely cosmetic for most cases. Granted, not all, SRV records are still a good idea.

However, on the wider internet with third party services it's much easier to manage and debug dedicated port numbers.