Is there a "Kessler syndrome" analogue for the internet, where failures beget failures until it's just an impenetrable cloud of fail, forever?

There's such a thing called the "Thundering Herd" problem, that partially matches.

From wiki: the thundering herd problem occurs when a large number of processes or threads waiting for an event are awoken when that event occurs, but only one process is able to handle the event. When the processes wake up, they will each try to handle the event, but only one will win.

Until someone smashes the "SEND MOAR SERVERS" button.

I can't see how this is the reason for HN to take 10 seconds for the response of the main page (I mean, the URL fetched from the address bar, not the subrequests the page does), as everything else downloads immediately.

The DNS entries should be cached by the browser (and the middleware), so that this problem should only happen once, but I get this constantly.

Also, I sometimes get an error message from HN, which seems to indicate that this is some backend issue which fails gracefully with a custom "We're having some trouble serving your request. Sorry!" on top of a 502 code.

It feels more like there is something else still broken.

In the case of HN it's probably just heavier load than normal. It's much faster if you're logged out.