Do you think a woman should have to change her last name when she gets married?

No. It was done originally to show that a woman, after marriage, no longer had allegiance to her maiden name or to her parental family, but could only have allegiance to her husband. That was important in the middle ages, when battles were fought over land and by clan. It also signified that a woman, after marriage, was the property of her husband.

It certainly makes it very difficult to do genealogy. In many cases, in the past, the last name of a married woman was considered so unimportant that it was not recorded anywhere. I can go back to the early 1800's and the attitude was, apparently, who cares what her last name was before marriage? Now those womens family trees are lost forever.