They absolutely do, but women who make a habit of storing things in their cleavage tend not to be the classiest women.
In between the breasts is a very sweaty place to put things. As
@Magicicada_septendecula observed, it's bad for electronics, it leaves paper money damp, and habitually keeping non-porous things between the breasts can lead to a localized yeast infection. Things can also fall out of the cleavage and end up in the band, or even falling out the bottom of the band if the wearer is active or the bra is poorly-fitted.
Bras with pockets, or the add-on bra pockets for wary travelers, usually use the side of the bra or the wasted area on the anterior shoulder. There's an empty area where the strap goes out from the...