Repeatability requires fair precision as to how much of what.
Having decent measures is also very helpful for correcting a recipe that didn't quite work out - you have a baseline.
They are also very helpful for persons who've never made the dish before, vastly increasing the chances of success on the first try.
Now, if you're a peasant with only 5 or 6 ingredients available, and you make the same thing day after day, you don't need measures. That's where the myth that measures aren't needed came from - but we aren't living in sod huts any more, at least not around here.