Perhaps this is true of some Platonic ideal of libertarianism/statism, but in the real world people who would usually be classified more on the statist side of the spectrum tend to also want the state to hurt people less in various ways.

I think we interpreted that claim differently; I saw "want government to hurt people less" as "oppose any government policy that hurts someone," rather than "oppose at least one government policy that hurts someone." I can't think of a libertarian policy proposal that leads to the government actively hurting someone more (though, of course, many libertarian policy proposals would make people worse off as the government moves from action to inaction).