You can certainly assign programs to open in given Spaces with no command-line folderol needed. But you can't have a set of icons sitting on each individual desktop (nor should you).

I for example have Safari set to always open in the first Space (desktop), and Photoshop to open in Space 2, etc.

The dock and desktop icons stay persistent on each desktop.

What I'd suggest you do is create folders of related apps (in the Applications folder) and then drag those to the right side of the dock (you might want to give each one a custom icon for better visual identification, see the picture from my dock below). Assign each "group of apps" to open in a given Space when launched.

That will accomplish your goal without cluttering up your desktop.

Custom-folders-dock.png