Why the power supplies limit the amperage?
Three things:


Current does matter in burning up the circuit.
Yes, for a given load that expects a constant voltage, you can attach a supply with a higher current capability* but the same voltage output, and everything works fine.
The supply can only give so much power (i.e., only so much current times voltage).  So if I try to draw one amp from a wall-wart that's only good for a quarter of an amp, then the wall-wart will either quietly shut down, or it'll burn up.


So the rule for most supply and load combinations is that you need to select a supply voltage that is within the range that the load can accept (or exactly on, by preference), and you need to select a supply current capability that is the same as, or greater than, the load's rated current draw.

* With modern wall-warts and supplies.  Confusingly, older wall-warts would actually supply higher voltage if you asked less current of them.