You can't decouple multiple windows of the same app.
IIRC it insists on disappearing if you are in fullscreen on another display.
It also wastes more space than other taskbars to be usefull and look decent.
(disclaimer: I dislike MacOS globally)
Why are programs still "open" when they have no open windows? Why am I able to cmd-tab to applications with no open windows and have nothing happen?
I'm a few macOS versions behind what's current, so it's possible things have changed, but historically in OS X/macOS your description applied to apps that could have multiple windows. Any app that could only have one window—for example, System Preferences—would quit when the one window was closed.
System Preferences (especially the iOS-ified version) breaks a lot of rules. The "classic" version is really similar to the System Prefs in Next/OpenStep. The classic version was a single document interface, and it used a back arrow to go back a level. The new one has more persistence IIRC with the list down one side.