Since when is the Piccolo Trumpet in your face? Sure, its "distinctive" because of its color, but it can be very tame and quiet, indeed, pleasant. Just check out Bach's Brandenburg Concerto No. 2.
In my experience, a true Trumpet player on a real Bb (or C) trumpet can outplay any Piccolo Trumpet in terms of loudness and audacity. Piccolo trumpets are not a replacement for the upper range of the Trumpet, rather a unique color tone that could be desirable sometimes, much like the Eb Clarinet. But that is just my experience...