showing a driver's license when buying a vehicle isn't required
because you don't have to have a driver's license to own a vehicle. You have to have one to drive it, but that's not up to the dealer to enforce.
OTOH, BATFE requires the FFL dealer to establish that you are a state resident of the state in which you are receiving the transferred firearm. Standard way to establish that is via DL. Your CCW/CHL won't cut it, because so many states have out-of-state permits; my FL permit started as in-state, but is now out-of-state. I notified FL as required, but they didn't ask for my old permit or mail me a new one, they just said "ok, we'll update the database" and that was that. Nowhere on my FL CCW does it indicate that I am not a FL resident.
So, the dealer will want to see your DL, to establish state residency. Depending on where you live, there may be additional requirements (handgun purchase permit in NC, for example). If you have a CCW/CHL etc, showing that can eliminate the waiting period for purchase.
In other words, don't blame the dealer. Blame BATFE and Congress, if you want, for limiting handgun sales to state residents only.