2-3A is very typical maximum rating.
This is indeed related to the mating of the socket. The contacts are tiny and do not have much force.
But if you just use short pin header, pins directly soldered on PCB both ends, I see really no problem with 6A. You can easily qualify the heating by a simple test since the uncertainty of the contact resistance is removed.
There still is a risk that if you buy another brand, they use different alloy with worse electrical conductivity, but if the PCB-PCB separation is just a few millimeters, it's quite far-fetched. The pins are thick, after all, and the PCBs will act as heatsinks. I wouldn't be surprised if you could pull of something ridiculously high like 20-30A, given the PCB tracks can handle this!