While the player has a great effect on the sound that comes out, I'd say the "one trick pony" designation lies in the bass itself. Across the same playing style, some basses don't change in sound much, If you wire a single pickup straight to the jack, the bass itself doesn't have many tonal option in and of itself. Basically: Less options=less tricks.
I've wired a single pickup straight to the jack and wrought many tonal options out of it.

