One would think with 5e's flat math that ASI bumps would be statistically significant, rather than something to be dismissed.
Define "statistically significant". If you're doing 1.05 extra points of damage per round and the typical combat is over in 4 rounds, how often does it matter when the amount you drop an enemy below 0 doesn't count does it really matter?
I will say that the spread of ability score difference between characters if you roll can be significant. Because you can end up with 1 character with multiple 18s and a 20 and another character with all numbers around 10 or below.