There are many cases where the law doesn't require specific performance. If you hire someone to work for you, they can refuse to come to work. You can fire them, but you can't force them to work for you. If you offer to fix someone's sink in exchange for them fixing your car, one of you could fail to do the work. The other could sue and get paid some money, but the law won't enforce specific performance and you can't actually force another person to fix a sink or a car.

By your reasoning we are not "free to hire someone to do work" or "free to exchange sink fixing for car fixing".

And even in the chess example, you can't force someone to play chess, and if you exclude them from playing because of their reputation, they still are not playing chess with you. Soi by your reasoning, we are not free to "play chess with person X", even if you argue that we are free to play chess provided we aren't picky about partners.

Note, that since monogamy assumes someone will only have one spouse ever, reputation is less useful.

It's true that someone cannot gain a reputation for being honest in monogamy, but they can get a reputation for cheating. It only requires the "can have a reputation for cheating" half in order for reputation to be useful. It still lets them cheat the first time, but they can always cheat the first time in a chess game as well.