This was an interesting thought. But for educational research, statistically speaking, as long as the differences are, in fact, randomly occurring then it doesn’t matter. It’s the non-random factors that were interested in. Those are the factors we can study and attempt to influence.
It’s true though that we can’t pick our teachers. But schools in socially disadvantaged areas don’t occur randomly. Research into both why areas become disadvantaged and how best to improve them can help alleviate the non-random aspect of being landed with a sub-standard educator (due to the difficulty of hiring high quality educators in disadvantaged areas) or educators that aren’t provided with sufficient resources to do their jobs.
Accept the random disadvantage because you know that it will even out over time. But fight fiercely the non-random systemic disadvantage.
It is good you brought up disadvantaged areas. A section on that could've been in this post. I did make a past post on the topic of some school are not able to get good teachers. I think one factor in that post was a lack of funds.