Sometimes people with 2 boys will try for a girl. That's the only legitimate reason for trying to have more than 2.

Well, in the case of a few people I know, it's because their parents are willing to essentially be "co-parents." Grandparents doing school pick up and drop offs, paying for school and camps, providing any kind of one-off childcare,
Cleaning up messes for parents, etc. if you have two (or in some cases four) extra adults around who help out for free, having more than you can personally handle becomes manageable.

Would I ever personally do this? Never.

In my larger circles I see and have been told that having more babies works for some SAHMS who do not want to go back to work once others are older yet feel badly not having a young one at home.

I have noticed that people who com from large families where they as kids were forced to take on a parental role with the younger ones, often don't want kids once married themselves or only want 1. Not always, but often. I think it is not fair to expect your older kids to raise the younger. a little babysitting here and there and some diaper changing and cleaning the house is good for teaching responsibility, but the parents should be doing the bulk of child-rearing. You have to willing to let your kids have an actual childhood and not be selfish.

Three is some new strange status symbol. Part of the I'm so busy! culture.