Why is "dragging it in" considered bad in small aircraft, but fine in larger aircraft?
For the GA fleet, there is some historical precedent operating here.  Years ago, engines were much less reliable than they are today.  Dragging it in generally means that you cannot glide it in if you have a complete power failure.  This translates to saying in the event of an engine failure, you are landing off airport with limited selection of landing sites (your altitude is low as you are now below pattern altitude).  So if you are flying behind an old Curtis OX-5 in your Jenny, a gliding approach to landing was recommended back in the day.  

Engines are much more reliable today.  After an analysis of landing accidents, the FAA determined that a stabilized approach to landing is less likely to result in an accident, and they changed their guidance accordingly. Stabilized approaches are partial power-on landings.  Some old timers and some old time CFIs reject the FAA's statistical analysis and still teach/fly glide-it-in landings.  Properly executed, both approaches to landing are safe.  It is just that the FAA thinks that stabilized approaches are safer given engines commonly in use today.  

It is also true that virtually all airlines require stabilized approaches in their operating specs, and that a go around is mandatory if the approach is not stabilized.  With this in mind, flight schools that aspire to send their graduates to the majors will all teach stabilized approaches.