Scott Christian
Hero
True story: I played a dex based barbarian wood elf. By sixth level I was running, I think like 150' or 160' feet a turn. I could run 110' a turn and still attack!There aren't a lot of barbarian elves because they don't get a bonus to strength. So playing one is out of the norm and memorable.
With floating ASIs it is no longer out the norm. It isn't against type.

But this combo can actually be an argument to keep the standard ASIs, as it can does a forced take on how to play a class, and sometimes leads to unique builds.