>Interestingly, electric cars become more efficient the slower you drive.
According to physics, that rather applies to anything moving through anything:
The velocity above is squared, so you double your speed relative to the air, it quadruples the energy required to overcome air resistance.
Where your point makes (more) sense is that there is a minimum amount of fuel needed to keep the motor turning over at low speed or idle, and this fuel is not achieving useful distance as it would at cruising speed. Of course it requires you to ignore things like headlights, air conditioners, CD players, brake lights and all the other goodies whose fuel requirements are not necessarily a function of the speed you are travelling.
On the original point, a detour will require more energy than you planned. Range anxiety is not so much caused by the km per charge, but the time to recharge. If my petrol light comes on 50km from home, I will fill up even though I know I would probably make it. That is because we are talking about a 5 minute inconvenience. If it meant waiting another 30 minutes, I am far more likely to risk it.