Hello. Not sure if there is a more current post regarding the screen saver issue as described by the OP, so I would like to at least give one very specific solution as related to the USB devices mentioned by Mr. Heaverlo. I have a Logitech Extreme 3D Pro joystick used for the game Elite Dangerous where it works great, ..however the only problem with the joystick in relation to it's main function is that it has a very slight but definite drift which you must compensate for so that the stick does not give unintended instructions to the game. The dead spot, wherein no output from the joystick is passing to the game while the stick is sitting in it's neutral position, is a problem on this nice but inexpensive game controller because the weight of the stick itself tends to make it fall off center by 4 or 5 degrees. In game you can make adjustments to ignore any input within that first 5 or so degrees of output from the joystick. This allows the joystick to do it's job without the player having to constantly adjust for the unintended input when they might need to release the stick.
My thought is that perhaps in Windows 10 the joystick is being treated as a general purpose input device akin to the mouse, therefore it is checked by the system even when there is no game for the joystick's use. Thus that small lean of the stick from true, that can be tweaked in-game but is still happening physically inside of the joystick is actually being viewed by the OS as a real-time real user input. This input, similar in effect to a bump of the mouse, causes the normal wake response which consequently interrupts the screensaver. In my specific case this USB connected device was the culprit.
I am a photographer and I like to have my pictures scroll through when the system is not in use; that and the fact that my family seems to think the best screen to leave the system on when they walk away is the brightest white screen they can find - lol Hope that helps or perhaps points some of the very knowledgeable people here to find a solution that doesn't involve the necessity of unplugging a device for a very common application to run.