In his second lecture on R. Chaim Ozer Grodzinksi for Torah in Motion, history professor Marc B. Shapiro says: As with most gadolim, Chaim Ozer comes from a rabbinical family.
This notion that people have that the great equalizer is the yeshiva and that Torah study could take someone from a simple poor ignorant family and make him into a great Talmud chacham (sage) and then he could marry into the highest families, it’s true in theory. Rabbi Yechiel Yaakov Weinberg did come from a simple family. He was one of the few. His father was in the army. The Jews who served for years, decades, in the army were usually the children of poor people. The rich kids were never taken.
If you came from the lower class, after your son finished cheder, he’d have to go work. The people who ended up going to yeshivas were from rabbinic families or from wealthy families. It’s a nice idea that anyone can rise to the top but it didn’t happen that much in practice.