Why can't I keep icons on a different desktop?

I have just finished browsing every possible answer on organizing desktop icons on a Mac. Some of the answers were outrageous, so stop answering if you don't have a proper solution.

So I need to move my icons around my desktops using Mission Control. Unfortunately, if I switch Spaces, icons are coming along. As far as I can understand, this is the default behavior. Is there a way I can have a CLEAN space / desktop where I could create other files/icons?

If that's not possible, the existence of Spaces is flawed. You either have another desktop, either you don't. One desktop is one desktop, not the same desktop with some app opened.