I always hate the terminology of “properly power” simply because it implies that many amps cannot do it. Which isn’t true. Many amps are capable of powering most headphones, but not all amps deliver power as cleanly as others at certain settings. I actually had this question recently and got a very lovely short essay from GoldenSound. It basically came down to, “just because an amp can technically do it, doesn’t mean that it does it well.” I think the best example that I can give is my Element 3 vs my Apple dongle when powering my 250 Ohm DT 770 Pro. With the Apple dongle there is a ton of high end hiss that that goes beyond what the 770 is known for. It’s palatable, but definitely not pleasant. But with the Element 3, none of that is present. Different topologies allow for some amps to work better at lower gain settings. Hence why the Apple dongle has sizzle and hiss, but the Element does not. Ideally, you want to introduce as little gain into your signal as possible since gain will color the sound before it even reaches your headphones.