This feature is likely to be perpetually “planned” as the Finder is so deeply embedded into the operating system.

To remove the Finder icon from the dock and application switcher:
1. Path Finder > Finder > Enable Finder’s “Remove from Dock”
2. Right-click on the Finder dock icon and select “Remove from Dock.” This works even while the Finder is running, allowing it to run silently in the background.

The dock’s trash can is hard-coded to use the Finder, so there’s nothing we can do about it.

This is somewhat experimental, but it’s working so far:

Cick on Path Finder’s desktop, then choose View > Show View Options. Click on Set Colors and mark “Use the Finder’s desktop window level”.