Yes, he may have missed the density a bit

but even your evidence agrees with him about the speed of electron travel. He said nothing about speed of EMF travel; be careful.
As to the battery example, care to put numbers on the conditions, please?
Well, I just destroyed a 1.5V AA batter for you with a 15" 24ga wire. Yep, it gets hot indeed. Know why?
E=I*R or, I= E/R; 1.6, if that battery can hold 1.6V with a .03 Ohm wire resistance which it cannot, but, that calculates to 50A demand from that little battery and through that 24ga cable. Of course it will get HOT!!! Pushing 50A through that 24ga, force feeding it.
In his example next to that 40 watt light bulb, well, I will let you calculate the bulb resistance compared to the wire. Oh, don't forget, he was using a 250V source.
Oh, here you go, the bulb is 1562 Ohms. Does that wire really matter much here? Really?