I'm not at all sure that the increased bra-wearing in
Europe is a sign of American culture being "contagious".
To begin with, I think western Europe is still much
more positive towards breast freedom than the US.
Women wear bras more often because it's fashionable
(both the bras themselves and the pushed-up,
exaggerated breasts that require either a bra or
serious implants), but fashion is multinational nowadays
and I bet European and Asian fashion influences the US
as much as the other way round.
And there's still a difference in attitudes: in Europe,
a braless woman may be considered unfashionable, but
not "immoral" or "scandalous". It's simply no big deal,
the way it seems to be in the States.