The flaw, as I see it, is that batteries make a lot of sense - when stationary. Dragging one or more around with you is where they become stupid.
The “battery” for your ICE car is actually the atmosphere. Oxygen is a tremendous energy source and is continually renewed in the atmosphere by the Earth’s plants. It turns out that oxygen can produce usable energy with a large number of easily accessible carbon compounds. Your ICE car carries one of these around with it. What it carries around with it is liquid, reasonably dense and reasonably safe. It can even afford to be grossly inefficient in utilization, since the atmosphere is helping to produce energy. When the energy is used up, so is the liquid.
An electric battery turns out to weigh the same, whether it is charged or empty. Everything needed to produce energy has to be carried. They are a terrible idea for a mobile power source, in my opinion.
You explained your point of view very well. I agree with it.