Not all trainers like training southpaws. A lot of times trainers either love that their boxer is a southpaw or they hate it because they don't feel comfortable training them. No one ever turns down an orthodox fighter unless they simply can't box.
There are lots of good southpaws doing well. Remember only about one person in eight is born left handed. Since there are about 7 times as many natural right handers as left handers there will always be more good right handed boxers than southpaws. There will also be more right handed bums than southpaw bums. There are just lots more righties than lefties in the world.
Andrade, Lara, Russel Jr., Rigondeaux, Saunders, DeGale, Stevenson, Glowacki (or Usyk is he wins that fight).
Those dudes are all pretty prominent in their classes especially taking all the names into account not just the ones I listed that hadn't been mentioned yet.