I totally understand that a motor draws more current when the load increases, that is a given on any inductive load. But we have fixed resistors on 3 of the speeds to control the speed, so on the 3 lower speeds the circuit is resistive-inductive. The resistor drops the voltage which in turn limits the current. This is proportional to the amount of resistance, so the more resistance, the more current gets limited. (We know that current is limited through the resistor because if it wasn't, the motor would simply draw enough current to maintain it's rated speed and the resistor would not slow it down). So I don't see how the lowest setting, with the most resistance, would proportionally draw more current than any other speed that is controlled by a resistor. One could argue that the high speed circuit, being basically all inductive, would be more likely to experience runaway current when overloaded as there is no fixed resistor in place to limit it.
The other issue I have a problem with is why aren't we seeing low speed meltdowns? Granted I have only seen 6 meltdowns but they have all been the high speed. 3 were Ford vans in a fleet where the high speed terminal on all 3 dash switches melted, 1 was on my 1987 Mercedes 300 where the high speed fuse melted repeatedly, 1 was my Jeep where the input terminal to the mode switch (where all the negative current passes) melted when the blower was on high. The 6th one is the one in this thread, which was the high speed terminal on the blower switch.
I'm not discounting your theory and this is an interesting discussion which I plan to research more. Do you have any examples of low speed meltdowns, or any references to your theory?