I tend to think that the problem may be with your graphics card (If you have one) or with the motherboard if you are using integrated graphics. One sign of a failing graphics card is random "crashes", where the screen goes black, and can come back on. They can also cause Blue Screen of Death (BSOD). If your card is older this is very likely. A thermal issue with the card can cause this. You mention high CPU utilization, which would make me suspect high GPU utilization as well on a discrete card, and even more of an issue if it is integrated graphics in use.
It is possible that the monitor itself is failing. It could be failing backlights on your monitor; a quick check is to shine a bright flashlight at the monitor when it goes black If there is still a dim image where the light hits the screen, you know the backlights or their power supply are probably bad. It pretty much eliminates your system as the problem.
I would do some of the checks below next. I'm answering mainly from the perspective of a desktop system,
A quick test to see if it is your system or monitor would be to borrow another known good monitor, or another known good one of of your own if you have one, and connect it to the computer in place of this one. If the problem reoccurs, then you can be pretty safe in figuring it is the computer (or cable), rather than the monitor. As jayeff said, monitors are dumb devices and they are very unlikely to be able to cause BSOD.
Also swap cables with a known good one, the problem may be a failing cable. See if the problem persists. If it goes away you know it was the cable.
If you have a discrete graphics card, also see if you can swap ports on the card. If your monitor has multiple available imputs you can try other feeds like DVI or Display Port, to see if the problem persists. It is possible for a port on the card to go bad. Not sure that your monitor is new enough to have USB-C as an available input.
Another thing that can cause erratic operation is a failing system power supply. Again, if there is an association with high CPU usage, that could be another cause.