My
dryer has no ground (technically, practically it has no neutral)

That exemption in the code (dryers and ranges) started in WWII to save copper.
A couple code cycles ago the NFPA decided the war was finally over and they
made these circuits conform to the rest of article 250 with a separate ground
and neutral. You will now see 4 prong receptacles being installed there.
I suppose the reason we never piled up bodies is because these were 30-50a
circuits with very small 120v loads, if one was there at all.