I'm no doctor or anthropologist, but in my opinion, there's probably NO benefits to that. If anything it's a drawback. There IS, however, a benefit to having a period. It keeps women fertile by shedding old gross eggs. Being emotional during your period or before it is due to hormonal changes in the body. It's kinda like smoking weed, your body all of a sudden produces a lot of dopamine to make you feel happy and funny.
Some aspects of human anatomy and behavior have no evolutionary significance, they are just random occurrences.
The nail on almost everyone's big toe is much thicker than nails on the other toes. That is true for me, but the nail on my little toe is thick like the one on my big toe. Only a minority of people have that.