The number of eggs women have is far from "quite low". How many do you think they need? A woman menstruates once a month until menopause, from say age 14 till 55. So you would estimate a need for 492 total eggs.

A woman is born with 1 million eggs, and has about 300,000 left by puberty.

Which is to say: developing the eggs is not a limiting factor in getting them from women.