Why doesn't Firefox in private browsing mode delete all browsing history. cookies, saved pages, etc. when the browser is closed?

Because when you turn on "never remember history", it doesn't save anything new, however doesn't touch your existing storages: bugzilla.mozilla.org/1476152

I have Firefox in permanent Private Browsing only,

How did you enable Private browsing, via settings or maybe a Window's menu item i.e. a GUI no manual efforts.?

I use 'normal' mode with settings to clear when I close, and that works fine

I enabled Private Browsing several versions ago, probably around releases 120.??? to 125.???. This is a guess on my part, based on long-ago memory.

With the most recent updates, Firefox just seemed to keep those settings. At this point, FF has become so complex and hard to use that I don't know how to turn off Private Browsing and put it into Normal Mode.

Based on the previous post (eight to seven years old), this seems to a a bug that never got fixed.

I have 8 different extensions activated in Private Browsing Mode specifically set to block trackers, and use the Strict / Do Not Fix settings. It's not giving me a good feeling that the amount of "cookies" and "saved pages" are allowed to accumulate despite all of the above.

I think I'll reach out to the Swiss software developers at Protonmail and ask if they will design a browser that minimizes the accumulation of trackers and cached pages and automatically deletes both when the broswer is closed. Shame there isn't a straightforward way to do this in FF.

I posted some videos to bugzilla.mozilla.org/2013262 so you can get some inspiration which setting to reverse.

If you want to delete things on shutdown (post facto, from disk), it's a different set of settings than not writing them in the first place (but keeping in memory until shutdown).

It's plausible that the "fire" icon in always–private mode does not necessarily nuke every type of storages so if you have a good reproducible example it might be worthy filing a bug. (Similar to the one here above, where always–private does seem to interfere with the usual browser UI since it's all only ever kept in memory.)

So I'd advise to change "never remember history" to "customize history", and then disable the checkboxes there, and also configure what is cleaned on shutdown, and let it clear on shutdown. If you want to clear during browsing, check the options to customize your toolbar to put the "Forget" button there if you want to have a quick access sanitization option.

Can you share what kind of storages are shown for you in the dialog after "burn" is performed? I just tested it, and if I haven't switched to that mode completely cleaned out, what's kept is kept (private mode does not nuke data from non–private mode), esp. internal browser data that's genuinely exposed in the sanitization dialogs as well — all certificate and trust data, home page caches, stories, wallpapers, that kind of stuff. If I went into that mode at 0kB the "burn" action effectively cleans out everything, just a few things quickly re–populate back — again, mostly internal things, favicons for shortcut tiles, home tab etc. … if only things that seem to occupy space is "temporary documents and caches", you're probably just looking at this internal data — open about:cache › disk › List cache entries … and the keys will tell you what's the origin of that storage +timestamp when it got primed (my guess: after you pressed the fire button).