I 100% agree with this - My screensaver will never work when my Logitech Extreme 3D Pro Joystick is connected to the PC (and has even caused driver crashes and general instability in the past).
Disconnect it - and PRESTO - Screensaver works and Win 10 is more stable...
It seems to be something to do with the Logitech app in this case constantly polling the joystick for it's current position/status.
Probably wouldn't happen with a stick that has active signal feed rather than positional polling. (guessing here)... (read HIGH END STICKS - lol)
I have even seen someone claim their mouse was causing this before - changed mice and it worked again. (repeated changes with original and different mice to prove it too).
Good info Richard.
Just start by disconnecting one device at a time, set screensaver timer to 1 min, restart PC, test, and repeat with each device.
If that doesn't work - do you use any 'Virtual Devices' particular to programs you use?
If so - disable that program and virtual device. - Rinse and repeat!
Many different apps and programs could potentially cause this, apps with overlays especially (Discord, Nvidia Geforce Experience, Mumble, Radeon Software, Hardware monitors, etc (the list goes on)...
Disable an app in your taskbar and test, try another... If none of that works... *shrug*
Hope this helps some people out there.