The freedom to be fruitful and multiply is one of the first to go when population densities increae.
Family branches in the old country had relatively small families on average. It was due to not marrying, late marriages, few pregnancies, and a lot of infant and childhood death. One branch had a lot of clerics, and they had large families. Apparently government enforced tithing gave them access to more resources.
Once the ancestors arrived in America, the families got very large on average until the last half of the 20th Century.
“Family branches in the old country had relatively small families on average.”
Yes, but all those reasons you cite to explain the phenomenon do not include “because the government imposed population limits on them”. They still retained the freedom to be fruitful and multiply, they just chose, for understandable reasons, to exercise it less than they might in other circumstances.