Tailwheels were usually necessary to give sufficient clearance for the prop without having a very long, and therefore heavy, undercarriage.
The main design advantage of biplanes is that the two wings with their associated bracing form a stiff but light girder. Once the trick of building strong enough wings cantilevered out from the fuselage had been sorted out, the resultant loss of drag gave greater airspeeds and the excess wing area was no longer relevant.