That's a kind of weak criticism. What functions are considered elementary was always going to be arbitrary, picking the set you can generate from exp, log, and some complex algebra is not the worst choice.

If nothing else you could solve simple differential equations with them. And it gives you the 'power' function.

The very fact that the set of functions is largely arbitrary is a much bigger issue. Or at least it limits the use of the fact that you can represent those functions.

Edit: I feel the need to add that just because it is a weak critique doesn't mean the argument itself is not interesting.