The logical problem is thus: what good does it do to say that they had rights, if the rights were ignored? It's meaningless. At least we, fortunately, have moved beyond that. And I would disagree with you that women were brutalized or frightened into giving up their rights too often in the America of the 1820s, as a close study of court records shows. Divorcing wives received child support and spousal support as well as fair property settlements. Such things were astonishingly common in an age which we think of as being pre-divorce. Women even in the eighteenth century were the successful proprietresses of their own businesses. You may be thinking of English law, which continued to be pretty unenlightened on the subject of women's property rights for much longer.
Divorce in the period you mention was rare, limited pretty much to the upper classes and generally granted only when one of the parties had engaged in really egregious behavior, in which case it is not surprising that the wife was awarded such settlements as an expression of society's disapproval of the husband's actions.
FWIW, Islamic law also generally requires a property settlement for a divorced wife, although the husband always retains custody of the children.
Perhaps the most appalling aspect of Islamic law for women is the ease and informality of divorce for the husband and its impossibility for the wife. American law has, I believe, always treated the genders the same in this regard, at least in theory.
I say "in theory" because a great many men will be glad to tell you at length about how the deck is stacked against them in divorce court. A good example of how "fair and equal" laws are not always applied fairly and equally in practice.