Not if it's applied evenly across the country, no.

When you're measuring schools you're trying to measure the impact of the actual school, not all the other factors, and to do that you have to separate out socioeconomics. Higher income parents are more involved in their children's education and can make up for a bad school in ways that lower income parents can't. It's pointless to compare schools to each other unless you adjust for demographics.

You could make the argument that not adjusting for demographics obscures the fact that some states are for some reason failing to teach certain demographics as well as Mississippi.

The more "adjustments" you do based on demographics, the more likely that one of your adjustments is incorrect and obscures problems or encourages incorrect solutions.

Controlling for demographics is done all of the time in social and behavioral sciences.

This is an argument to extremes, and it falls apart when you go to the other extreme: if you refuse to make any adjustments then you're now unable to separate the marginal effect of the school from the much larger effect of socioeconomic status. This would likewise obscure significant problems and encourage incorrect solutions.

The correct approach is to adjust for demographics but do so carefully, rigorously, and consistently.