Do you think all women should freeze their eggs?

That actually brings in more ethical problems than most realize (good question by the way) because of what is to be done if they are never fertilized.  Are they a potential life being only 1/2  of the fertilization process? When do they get tossed or how long are they kept? Can they be given away or sold to another person?

Anyway, whether she should freeze her eggs or not is something to be seriously considered. If a woman is not sure when she wants to have or bear children, or even if she finds out later she can't, she would have her own DNA in those saved eggs.

Also, in the future,  I can see the strong possibility of some types of formalized international "egg banks" which will allow women or men to choose eggs as well as sperm for a more designer choice in the population. It may not be Science Fiction any longer much sooner than we think. (There are those now, but I am speaking of a large formalized global resource)

No. Most women can have kids without any issues. And for many freezing and then using them later is cost prohibative. Unless there is some sort of family history or medical issues I think it is a waste of time, money and resources.

Why would all of them have to? It's optional if they want to or not.