Is that so?
It was propheised at his birth (so the legend goes) that he would either become an enlightened teacher, or a "wheel-turning" world monarch (chakravartin). That doesn't prove he wasn't a royal prince, but then I guess I'm not sure exactly what a "prince" is.
In an oligarchy you can still have powerful military rulers "whose chariot wheels roll everywhere"
To continue the comparison with the Roman republic. Consuls where great leaders bestowed with great power and honoured for their military successes. The Roman republic had a taboo of monarchy, one that Caesar himself played with dangerously and which got him killed.
Prince comes from princeps (the first), a title used by the Emperor Augustus.