Does wire gauge significantly impact the charging rate of smartphones?
The contention is absolutely true.

AWG 28, often used in USB cables, at 2m is about 0.5 Ω either way, and charging at 1A thru such a cable would require the phone to draw 1A at 4v, which won't work.

At 2A it would be even worse.

The current situation is unacceptable, and USB cables offered should never have a resistance greater than 0.1Ω either way, regardless of length.

To check in reality, buy a USB current/voltage meter insert device. Usually about USD4-5 on EBay.