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It is not so much the assumptions. You need a more careful approach. Do not rush from observations to "easy" conclusions.
The mechanical model does not fit here.
If it were kinetic energy, the outcome would be very weak because of the electrons low mass. Also the electrons do not change their mechanical speed when there is electrical resistance.
Take a good science book that explains the basics and gives you the correct formulas to do such calculations.
Had I "concluded" anything, I wouldn't have posted in the first place.
Reading up on the subject at my local library is on the agenda. I just have get tired of programming first. 🤣
You are right about kinetic energy having low effect. However, in microelectronics becomes an issue, called electromigration, where the material laters are so thin that this small effect of electrons on metal atoms (the electron wind force) causes erosion, basically, movement of atoms.
And the effects on the micro wires are. really something. This errosion takes time of course, but not as long and the effect rises exponentially at the end because the current density increases.
It kinda blew my mind during my elec. eng. studies. Anyway, just wanted to donate my two cents on this matter.