Not all servers will provide an HTTPS connection, or accept your request for one. Actually, many won't.
The issue that really brought about this feature was that some *banks* (Bank of America being one of the biggest examples) and other critical sites would serve you a login page that *was not in itself secure*, even though it *sent your login info* over a secure connection. The former makes it easier for a MITM attacker (Man In The Middle - I know that you know this acronym, but for other readers) to send you a phony BofA login page -- with their phony black "padlock" by the login boxes, even though your browser won't show one. This feature forced the login page itself to be sent over SSL. Most financial sites have fixed this, due to the publicity.
I just tried picking a random, non-sensitive site from my bookmark list and adding it to Force HTTPS. Fx returned an error, code 12263.
I see that arkivmusic.com has a login page that is insecure, so you're right to force security. But I've seen other sites that, once you're securely logged in, do their product searches on insecure pages (to save bandwidth, presumably, although it isn't really that much these days), but so long as they return you to a secure page when you're ready to buy, I think you're OK.
I just logged in to retailer newegg, securely, but as soon as I went to the Home page, to search or shop, it was back to plain HTTP, although I was still logged in. Here's where it's important that the SSL login cookie be secured, too. Didn't buy anything, but I know that when you do, you're back to secure. And even secure for the logout page.
You could email the webmaster and ask for a site enhancement of all browsing being secure while logged in. Might or might not work.
Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:22.214.171.124) Gecko/20081217 Firefox/126.96.36.199