Dominion I've been thinking about this..
I hate to keep referring to wordpress.. but they have a wp-cron.php file that when run, causes it to "update" - so to speak. By default, every action you do on a wordpress site causes wp-cron.php to run.
This is really, really inefficient but also moderately effective and as you might mention - very out of box supported.
The problem is, php programs have no sense of time. It is a server-side renderer that generates html pages. This is worsened by the fact that flarum doesn't even refresh when you go from page to page (this is why notifications don't show up until you refresh the page - I noticed this for much longer with noscript).
Because of that, it's impossible for flarum to mimick what a pusher service provides. Any attempt will have to be a hack (like wp-cron.php) and be hard-coded to pull content on certain clicks. Should it do it on every page scroll? Clicking on discussions? Doing nothing would result in nothing ever showing up as a notification and is almost guaranteed to result in slower page loads (since it's doing more) and potential scaling issues (flarum-cron.php being run every half second on a busy site?) something has to tell flarum that something has changed, please run code to update it.
Both toby and franz are devs that know magnitudes more then me about php coding, so maybe they have some idea of circumventing wordpress's (and piwiks) best implementation of dealing with the php and time issue.
But as it stands, I'm sorry to say this, but if you're on a shared hoster, or simply don't want to know how to start and configure services outside of a webserver, you're going to be stuck. There are solutions, but I wouldn't call them optimal :\, or even if they would work as a forum notifier..
I'm aware that pusher is planning to be rewritten, but it looks like it's primarily focused on other components. I'm hoping it can be slightly modified to permit designating a ip address and port @Toby. If they both follow the same protocol, then it should be a drop in replacement (pusher.com -> slanger, etc) and I can get to testing how well it works, bugs, etc.