I believe the 'harm' here is that the USPS isn't allowed to set internal policies for how to operate. Such as the USPS being allowed to set policies on what they can/can't mail. This might mean that their rules around refusing to ship some items (e.g. explosives, hazmat, air bags, mercury, etc.) might be blocked as that's not an 'illegal' substance or whatever.
To be clear, I don't agree with this ruling, since I think this blocks a state's ability to operate their elections as they see fit. There's also no reason to block the mail as it's not dangerous or illegal. So, I think the court missed the mark here.