Wow.
I really do think that good-size families are one big factor in vocations. If you just have, say, one son, some parents wouldn't encourage him to be a priest because they want grandkids to carry on the name.
I don't have the research, but I'd bet you a beeswax candle that a disproportionate number of priests in the past came from families with 3+ kids.
Not all, of course. There are wonderful priests who were "only" children. But it's a factor.
My pastor comes from a family of 7 - 6 boys and 1 girl.