One thing I’m constantly doing when searching through my roster is filtering by class. Normally you are trying to determine which heroes to level based on their class as you might have emblems available for certain classes more than others. This works perfectly for heroes without a costume. However heroes with a costume are filtered by the costume that is equipped NOT their base class.
I would propose that by default it would be an IMPROVEMENT if this always sorted by Base Class as this is the most important use case. However it probably would not be too difficult to add some setting (e.g. checkbox) that toggled the sorting by base class or equipped costume class.
The only workaround right now is to equip the base class for all costumed heroes. Given the size of current hero rosters this is pretty unwieldy. Otherwise you have to commit the base class of every costumed hero to memory which is also nearly impossible.