Does 'small holes' mean 'mesh'? Don't forget that there are high voltages present in monitors - a mesh cover may be intended to prevent accidental contact and electric shock.
EMI performance is a black art - my experience is that various known measures are used to ensure a device passes a test. There's a test for emissions, and one for susceptibility. Because the testing is expensive, there can be a tendency to blanket the problem in the interest of expediency as opposed to detailed design based on engineering. 'Suck and see' engineering.