I wonder what it would be like if there was a setting in Firefox that opened each website in it's own container without any faff. Firefox automatically creates the container for the website if it doesn't already exist and opens the website within it.
You can pretty much do this with Firefox. I'm on my phone but ublock origin can block 3rd party cookies and scripts. This breaks a lot of sites but it also lets you turn those back on, on a case-by-case basis. Plus various other Firefox settings.
Like Linux, I don't want it to be the hobby; I just want to use it. If every website opened in it's only container then there is no care about cookies because they can't track you across the web, nor can they try to steal others.
Is uMatrix developed again? Because, since it didn't update webextension APIs, it got much less effective than uBlock Origin with a medium blocking setting.
I've only got superficial knowledge on this, but I believe Firefox does roughly that out of the box.
The feature that you're asking for is called "first-party isolation". It was implemented by the Tor Browser devs and upstreamed into Firefox, and it's what the whole Container technology foots upon. You can activate it in Firefox by setting privacy.firstparty.isolate in about:config to true.
But as I understand, Firefox now ships dynamic first-party isolation (dFPI) out of the box. Which is FPI, with a few exceptions to ensure web compatibility.
This is part of a wider effort called State Partitioning. And they market it to users as Total Cookie Protection. It's a bit confusing...
Your method would annoy me because of having to log in to websites 'all of the time' instead of allowing at least some to have persistent logins. Losing website preferences would also be annoying.