When you say mains-powered suppliers, if you're referring to a bench supply or something with a transformer in it, yes, that works (and is what I'm using now) but is impractical in terms of size and weight. I'm looking to make something that weighs no more than half a pound and is about the size of a human hand.
Indeed pushing the hardware to its theoretical limits usually ends in disappointment and pieces of plastic flying everywhere but I was running about 6A full duty cycle and everything was happy so for 4A I should be ok.