I don't think every woman should.
Did you know that even during the eras that corsets were popular and downright mandatory, if your stomach was too flat, the likelyhood you would be married got a lot smaller? A perfectly healthy woman for the 19th century was one with this type of frame:
small to moderate on top
rounded belly - not fat, but rounded.
It showed that you were healthy - had some meat on your bones and could adequately carry a child to term, and by having ample hips, child birth would be easy for you.
The first is accurate, but sometimes, there's just that stubborn pregnancy, or a turned baby, or some complication that even if you had hips the size of a cow, you could still have a difficult birth.
The girdle is a later invention when every woman seemed to think she needed to have the perfect 36-24-36 body - which very very few of us have.
I rarely wear a bra, because I'm of the smaller endowment - why would I wear a girdle?