Although I would welcome the use of common names instead of Latin names, the names in anatomy and pathology are annoying but not a hindrance. The difficult thing is to remember causes and symptoms of diseases, innervation of muscles, drug pathways, etc. That would be hard to simplify.
Instead of Latin/Greek root words, you'd have to learn a new system of common words. And not just new trainees, but also practicing physicians, because everyone has to speak the same language.