If you wear a bra that's of the right fit/size, breasts WON'T sag as much as if you go without one. Some have built-in support bands underneath them, which are better than the wired type and shouldn't leave marks or indentations on the skin. they can also help with posture and shape.
I totally disagree that it's a myth regarding corsets, though. In my great-grandma's day, after she'd given birth, she had a towel pinned round her stomach for so long, which helped to control the lax muscles. This was advised by her doctor, and a good few children later, photos show her to've been slim and shapely. The same with my mum, who was pregnant 8 times but who gave birth to 6 full-term children. She said that she wore a panti girdle after having her babies, and then as she exercised naturally, she lost the flabby bits.
Wearing control garments is, for many women, a common practice, so that their clothes look better. Meanwhile, their stomach muscles are supported and held in. It doesn't cure the problem of having a fat stomach, but when a woman chooses to wear these garments all the time, she knows it's time to diet and exercise - or not, depending on how she feels about herself.
A woman with fat around her stomach, will often prefer to be held in, rather than walk around holding the muscles in all the time. That'd be the best way to strengthen them, but for very many, wearing a good control garment does the job for them, and it's a definite "need".