I realize that the notification is there on a hard page refresh, but I would like to avoid refreshing the page to see that I got an answer or comment.
The cost/benefit ratio on this is kind of out of whack.
While we could reduce it on question pages, those are the only ones with a regular poll going on; every other page would gain a new background poller (or long polling, or whatever*).
That's a lot of potential load for marginal gain.
We may revisit this if we find more compelling "polling everywhere" features, since we could piggy-back on those requests. But for now, this is status-declined.
*Fetching the number is cheap, the # of connections is the nasty bit w.r.t. scaling.