I'm okay with removing ASI, but I believe that the races should still have strengths and weaknesses.
4th Edition did a pretty good job at giving most PC Races abilities which leaned toward a particular role without locking them into one.
For example, a 4E Dragonborn could use their innate abilities to occasionally cover the controller role or take out a group of minions. That was useful regardless of class. Sure there were still races that fit certain roles more easily, but even playing against type typically had reasons for the powers and abilities to be useful. Playing against type meant approaching the role differently, not suboptimal.