Question: I've installed Ubuntu 20.04 LTS fresh and noticed these keyboard shortcuts are not working when on desktop : SHIFT+DELETE, CTRL+C/V/X.

Any ideas what might be the reason?

Answer: 
The underlying reason why keyboard actions don't work on the desktop with recent versions of Ubuntu is that the desktop icons aren't handled anymore by Nautilus but a GNOME Shell extension called [Desktop Icons](https://gitlab.gnome.org/World/ShellExtensions/desktop-icons) which is part of Ubuntu's default installation (DEB package `gnome-shell-extension-desktop-icons`).

The motivation as well as some technical background for this design decision can be read in the blog article [Nautilus desktop plans](https://csorianognome.wordpress.com/2017/12/21/nautilus-desktop-plans/) from 2017-12-21.

A corresponding Ubuntu bug report can be found [here](https://bugs.launchpad.net/ubuntu/+source/gnome-shell-extension-desktop-icons/+bug/1813441) which also mentions possible workarounds.
If the problem wasn't there already when you started the PC session and appeared somewhere in between, then try to log out and log back in to your account. That pretty much solved it for me. If not, I hope more knowledgable users show you the right way to do it.