Do you want the days of the month to start with 0 as well? November 31, 2004 followed by December 0, 2004? A year is an ordinal number, not a cardinal number. I explained it earlier. This is the 2004th year since Christ's birth. The first year he was alive is the First Year AD. A year is a span of time, not a point in time.
I don't understand the antipathy to the concept of a year 0. As far as I can tell, the only objection, and it's a valid objection, is tradition. Some folks like a little clunkiness in their dating systems.