It wouldn't work.

Do you really think people get married and know it won't work out? Making divorce illegal would just turn marriage into more of a trap. What is worse, the kid having his parents divorce, or the kid having his parents hate eachother for the rest of their lives, always fighting and cheating, possibly in extreme cases one of them murdering/hiring someone to murder their partner so that they can once again have freedom.

If you want to make something illegal to stop the problems you're talking about, idiocy would have to be illegal. Either that or selfishness, or irresponsible people having children.

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