I doubt we would get more prospective partners, there seems plenty of them already. If we cannot marry them already there would be a reason for it that would be unlikely to change.
I want no lawyers in Skyrim thanks, so no divorce.
Personally I am not that interested in marriage, only one character has tried it out so far. Now if something happened to that lucky chosen one, being able to remarry would be nice. Especially if someone is planning on putting that partner in dangerious situations while in the players home. Usually staying at home is considered safe, something happens to the partner I do not want to be leaving any children at home alone.
I would also like my character to be able to remarry if something happened to the partner while out adventuring, there could be conditions attached to that, if they do not want us 'accidentally' losing any unwanted partners.