All that speaks to the point that the underlying protocol does not matter that much. The larger design is a more important consideration than the specific push tech.

None of this favors SSE, or anything else for that matter. You still have to think about bursting / thundering herd behavior after server restarts, which would affect any protocol. The browser auto reconnecting doesn't mean you can assume the connection remains alive indefinitely if a reconnect hasn't happened; you may want periodic notifications as a keepalive to enable more immediate recovery. Long-lived server state introduces its own distributed coordination and cleanup problems, which strict request-reply polling sidesteps entirely. Etc.

There is no silver bullet, only tradeoffs in the design space that need to be matched to your application's requirements.