This is actually an interesting bug which also happens for me and probably has some more info to be given.
When Roblox player app updates, it also creates a new Studio link in StartMenu/Roblox/Programs. This link is not bound to RobloxStudioBeta however, it’s bound to RobloxStudioBetaLauncher (I’m on mobile I think this was its’ name - will verify these once I’m on PC). I don’t know how this executable file works but as far as I can see it verifies app files when it’s running and also creates a desktop icon.
So, how is this related with OP’s bug? When users want to launch Roblox Studio some prefer typing “Roblox Studio” in Windows search bar (probably OP does that since they delete the shortcut) but problem is there are two Roblox Studio shortcuts, one gets created with updating Roblox Player and one gets created with Studio updates/installations. If the one which came with Roblox Player update shows up first this can happen.
This is is very annoying for me; I do not delete the shortcut from Desktop, but rather move it into a folder within Desktop. I always use the Windows key to pop up the menu and start typing to open programs (requires zero mouse interaction). With this bug, I end up with invalid .lnk files hiding the real Roblox Studio shortcut:
It’d greatly increase my experience if this was fixed!
Still a problem, and a very annoying one. As someone who likes to keep a clean drive, I’m literally forced to have these shortcuts installed whenever I run Roblox/Roblox Studio.