Without changing any other mechanic, they could still make it work and not confuse people not wanting an extremely needed fix...
Say my Fire type Pokemon has Blaze Kick, retyped as a Fire/Fight type move... And I'm fighting your Normal type Pokemon... Using Blaze Kick I get the STAB bonus from it being a Fire type move and the SE of Normal being weak to Fighting type.
They could just make it like that... The best one is the one that factors in... So my Fighting type could also use Blaze Kick on your Grass type Pokemon, getting the Fighting STAB and the SE effect of Grass being weak to Fire...
Or they could go with a better and more complex working system that everyone hates at first, but later realize is better later on, then accept it...