Well of course divorce rates were lower... If one is not allowed to divorce, one stays married. The question is not whether people stayed married, the question is whether people were happy together.
Beside that there is an issue with the institution of marriage. Lynne Fees mentioned that it was rather about purchasing a mate, which was not true all of the time (marriages out of love were made), but the institution 'marriage' did imply a family unit with children exclusively from the pater familias (what man would want to care for the off-spring of possibly another? It is still an issue and the reason why it is more difficult for a woman with children to find another man than it is for a woman without children to find one) and recognised by everyone.
But the marriage purely out of love is a fairly new phenomenon. Before a marriage was something to unite families, a political tool or even diplomatic. The Dukes of Burgundy were very good at that. Cleopatra was not afraid to do it first with Ceasar and than with Mark Anthony, if it could save her empire. Unfortunately it did not, but it could well have worked. The marriage out of love and love itself became a real obsession when the Romantics took over literature and poetry. In the times of Shakespeare tjere used to be love-poetry, ad even before that, but marriage was not really a part of that. Donne wrote poems to his mistress. Marriage was business and love was for outside of that. Marriage produced legitimate children, mistresses preferably produced none, or otherwise they were cared for but did not have real rights. The romantics paired up the two. That is where we get our image from, but maybe it is too rosy. I have the impression it is. Marriage is not being in love which stays for ever! It needs careful attention, like a contract, in order not to break it. Love provides a good base, but living together is not the same as going to your boyfriend and spending the day with him, or even the afternoon. That is I think where most people go wrong. They do not want to try to work things out because they expect it to be a marriage in true romantic style.
Marriage is as old as society is, only our image of it has changed and that is why we divorce and older cultures did not, or rarely.