Let's say I have just two monitors. That box being checked means I have spaces A1 A2 .. An and B1 B2 .. Bn, and monitor A can display any of the "A" spaces and monitor B can display any of the "B" spaces. But if I want everything from B2 to get displayed on monitor A, I have to create a new space An+1 and drag everything over one window at a time, like a cave man.
Unchecked means I have spaces AB1 AB2 .. ABn, and switching spaces switches both monitors at the same time! So if I want to see the A side of AB1 and the B side of AB2 at the same time, I'm out of luck.
Xmonad workspaces allow me to do any of the above behaviors (oh, and it switches workspaces instantaneously, instead of this left/right spatial thing macos insists on, I guess because of the trackpad swipe gestures). One of these days I need to try to make Hammerspoon fake workspaces in a way that works for me, because (like the OP) this is by far the least comfortable thing about working in macos for me.
If your state is A1/B2 (two monitors A and B displaying spaces 1 and 2 respectively), and you're working in A1 and want to switch B2 to B3, how do you "focus" on display B before moving spaces to B3? If you just press mod-3 I assume you'd get A3/B2. Do you have to alt-tab until you focus a window that is currently in B and then mod-3?
True about indexed access; some other window managers have natively built in "tagged workspaces" where windows have tags and the "chat workspace" is just "all windows that have the chat tag". You can (probably? I've never used them) bind numbers to tags permanently or temporarily but you wouldn't be limited to 0-9. I never bothered trying to copy that setup in xmonad because I never used more than 5 or 7 workspaces.
That's...not true, though? Unless I'm misunderstanding what you're after...
When you activate Mission Control (not sure offhand what the default shortcut is; I have mine set to Ctrl-Up, but I might have customized it), you can drag entire spaces between monitors. I do this regularly.
For me it's a two-finger double tap on the mouse (I think--not at my computer at the moment.)