I don’t know anything about atrophy and ligaments, but I do know that I wouldn’t go around recommending everyone wear a bra all the time to prevent boob sags, because it’s pretty much highly unlikely to have any effect.
When I went through puberty a friend of mine told me I ought to wear a bra to bed every night to “keep them perky” and I did for a while and then I gave up because it was just silly and I hate bras.