But Rawls is talking about distributing resources, not just making miserable people "feel better." He explicitly rejects the idea that basic liberties may be infringed by appeals to greater equality.

For maximin to be used in the way you're saying, we'd need a pretty bizarre scenario, one where, for instance, a single person has a terrible disease that can only be cured by more money and resources than all the money and resources of everyone in his Rawlsian society (anything short of that extreme would mean we could spread the cost around in a less onerous way; it would take a pretty big cost and a pretty small pool of resources to get close to making "many people much worse in order to make the life a single person marginally better"). In addition to being outlandish, it seems like such a specific situation would fall outside the very general considerations of the original position.