You make it sound like his only reason for disliking the notion is silly tradition, but there are some fairly rational reasons to avoid it.
It has a very broad, flat range of randomness. While a 1d8 doesn't vary the total damage by much, a 1d20 will range from "won't kill a kobold" 1 to "take a chunk out of a dragon" 20, and because the probability with one die is flat, they'll both happen with regularity. The end result is that hitting someone no longer becomes the important hurdle. You have to hit that person, and then assure that your damage isn't strangely negligible.
Doubling up on dice give the probability graph a curve to it, which gives a greater sense of what one can expect with a hit. Compare 2d10 to 1d20. They have similar ranges (2-20 vs. 1-20) but 2d10 scores its lowest value 2 only 1 in 100 rolls, and its middle value, 11, 1 in 10 rolls, so 2 feels like a calamitous failure, and a 20 feels like a stunning success, rather than something which happens all the time.