- that the 7805 can be used as is to drop the 12v to 5v,
Wrong
- that one should add 2 capacitors to the step-down circuit.
Right but not for the reason you quote, the capacitors are for circuit stability, they stop it oscillating.
There is no difference in safety, 12V and 5V are equally safe. Remember a child's train set has 12V exposed rails.
Local regulation however is better to minimise line volts drops.