Would you mind sharing what this "power distribution box" is used for? Just because it *can* pass 6 amps, doesn't mean it will in it's designed use. What is it designed to feed?
No matter what, the switch is only rated for 33mA at 12v, so yes, it's a poor choice if it's wired in series with the load.
EDIT: In fact, half of the switches capacity will be used just to switch the LED in the switch itself. That makes no sense whatsoever, you must be missing something. Are you sure there are no other switching components in there? (relay, mosfet, Etc.?)