The primary reason for a biplane is structural. The cross-braced wires are strategically placed to carry lifting loads very efficiently. A cantilever-wing monoplane needs a relatively heavy spar to carry the loads; a braced wing can be lighter.
And a well-designed biplane can have a very good roll rate. The Waco Taperwing of the late 20s had tapered-chord wings (wing mass concentrated near the fuselage centerline, thus low roll inertia) and ailerons on four wings (lots of roll power), and was famous as an aerobatic ship.
A ship with sweepback (Pitts, Great Lakes, Ryan PT-22) will snaproll faster, because one wing has its sweep effectively cancelled, while the other wing has increased sweep and thus less lift. I inadvertently snapped a PT-22 while attempting a cross-controlled stall. Never saw the horizon rotate so fast in my life!