9V 2.1mm(M) AC Adapter?

I don't understand how driving the Arduino with, say, a 4A supply is less safe than driving it with 550mA.

Try fiddling about and getting a short. Four amps is going to melt a lot more that half an amp.

If the Arduino tries to draw more than 500mA, and it is a normal Arduino, it's onboard polyfuse would (temporarily) blow, protecting the whole system.

Which poly fuse is this then? I haven't got one on my arduino.

Anyway a poly fuse takes a long time to blow so is no good at protecting semiconductors.