Trying to open Premier Pro, I get the above error message. My answer is "No. Absolutely not." Why on earth would I give any app whatsoever access to my entire documents folder, desktop and downloads? But it won't open otherwise, so I need a workaround. Fast.
Premiere Pro stores it's own folders of information in those places. For crying out loud, it doesn't read anything else. But your user profile with all your custom workspaces, your keyboard shortcuts file, your list of recent projects, all that stuff is what's stored in there. Your "local" Creative Cloud files ... all sorts of things Premiere needs to operate.
So ... you have to allow Premiere Pro to store it's files there. As you may be aware, many other apps do also.