@Circuit fantasist. Basically, I like your point to present and explain electronics from another angle; unfortunately it's an art and a gift given to few persons. When I was teaching math at the university, I thought once to do something similar; this was a fiasco, and that made me understand why the good old definition-theorem-corollary pattern has been used from 2500 years. (continued in next comment).

I've read your answer 2 times and have understood nothing. More specifically, your approach necessitates a good deal of visual information to make things intuitive, which is your mission. I would suggest to add schematics, a lot of schematics, inside your answers, in order to illustrate your ideas.

@‭coquelicot‭, ‭Thanks for the sincerity. People like you make me drop everything else and try to explain the philosophy of things to them... but it takes time and room…and not bother me with "no discussion" warnings. Usually, I richly illustrate my answers but here I assumed that everyone knows what 'tug of war' is. Olin's answer is perfect and I just wanted to visualize it by colorful words... and share some observations...

… Most electronic circuits (probably > 90%) are based on this humble network of two elements in series supplied by a voltage source… because they handle voltage; the old voltage divider is the simplest example. Besides this classic viewpoint, we can think of it also as of two voltage sources (the one with Vdd and the other with zero voltage) connected through resistors to a common (middle) point - the output...

… The upper (Vdd) sources current to this point thus trying to increase its voltage and the lower (ground) sinks current from it thus trying to decrease it. As though, the two sources "pull" the common point in opposite directions - up and down… (I will finish my response later since now I have to go to the lab where my favorites already are waiting for me)...