If men could get pregnant and have periods, they would be women. They would think, act and make decisions as women. The world would continue to be organized as it has been only with men taking the place of women.
What you are describing in your original post is your concept of an ideal world. One reason that an ideal world does not exist is that everyone has a different version of what they consider an ideal world. Your ideal world may not be my ideal world.
Another impediment to such a world would be practical impossibility. Has anyone invented a flawless method of contraception? Can abortions be performed safely in a drive-through facility?
Further, you are supposing that men have some unique ability to create an ideal world that women lack, and that if men could experience life as women, they would create what you consider an ideal world for women.
If men have this unique ability, why have they not already created an ideal world for themselves? Have you convinced yourself that the world as it exists is ideally organized to suit men?
If that is what you think, it is your prerogative to think so, but I think differently.