Why is barrier potential of Ideal Diode zero?
Because the "ideal diode" is meant to only model the most important characteristic of a diode, which is its rectification effect. The forward voltage is considered a secondary effect that is ignored due to idealization. At higher voltages (24V upwards), which were common in the days electrical circuits started spreading everywhere, the drop can in fact often be ignored.

If you are using a diode as a voltage drop element, and it is always forward biased, you idealize it in a different way, as a voltage source of 0.6 to 0.7 volts. In this case, for theory it doesn't matter that your implementation of the voltage source is a diode, so you call it an (ideal) voltage source instead of an ideal diode.