The B737 doors do entail greater drag. The B737-100 didn't have doors to save weight and also because there wasn't much room. Over a short-haul sector the benefits of low weight are more than low drag. The B737NG has the same arrangement to save weight and to give commonality with older models.
Basically, there is no real disadvantage for short-to-medium haul sectors for an airplane with no gear doors due to saved weight. It also reduces maintenance costs, though some suggest that there is increased damage from FOD.
Either way it is a minor issue. If it were a better system, however, I daresay that more airplanes would have this arrangement.