While all options are open in any emergency, speed and safety of recovery is key.
One negative factor of using engines is that frequently you may already have deployed lines overboard such as the life sling or sheet lines fall overboard and while keeping an eye out for the MOB you could foul your prop and possibly rudder by overrunning the rescue line then your dead in the water with no helm control. The other is when motoring in a MOB situation, with your sails still up you have a far greater chance of having sails and lines contributing to additional risk for crew that is concentrating on a MOB Rescue and not the boat they are on.
I've had the opportunity to view from a distance two MOB rescues and both were sail boats who used engines to return to the MOB. Both did a direct down wind run to the MOB with sails initially flapping and as they neared the MOB at least one sail partially filled giving the boat headway even when they were attempting to stop for a pick up. One drug the MOB 100's of feet before 3 large guys were able to pull the MOB in. The other did better by swinging clear of the MOB and approaching from down wind. They did almost loose it again in the process of the actual recovery as the boat naturally swung around and started to pick up way as the sails partially filled.
While doing a pick up with sails only would not have always prevented these situations it would have at least had the helmsman paying more attention to sails than only the motor controls.
Lots also depend on sea conditions and your specific boat.
Everyone should practice MOB in different situations using various methods to the point where you feel you can effect a rescue with several alternative methods depending on the specific situations.
I prefer a sailboat to a motorboat, and it is my belief that boat sailing is a finer, more difficult, and sturdier art than running a motor.... Jack London