I've always heard Qalgs for chemistry compared to classical methods though. Why do you think chemists are using CCSD and similar methods rather than the FT-ICR mass spectroscopy?

However, before WW2 one could have made such transistors that worked only by great luck, and they would have stopped working soon after that.

The reason is that before WWII it was not understood how greatly the properties of a semiconductor device are influenced by impurities and crystal defects.

During WWII there was a great effort to make semiconductor diodes for the high frequencies needed by radars, where vacuum diodes were no longer usable.

This has led to the development of semiconductor purification technologies and crystal growing technologies far more sophisticated than anything attempted before. Those technologies provided high-purity almost perfect germanium and silicon crystals, which enabled for the first time the manufacturing of semiconductor devices that worked as predicted by theory.

The publication of Shockley's theory has been necessary for the understanding of the devices based on carrier injection and P-N junctions, like the BJT and the JFET invented by Shockley.

However you can do very well electronics using only devices that are simpler conceptually, e.g. depletion-mode MOSFETs, Schottky diodes and MESFETs, for whose understanding Shockley's theory is not necessary, which is why they were reasonably well understood before WWII.

Before WWII the problem was not with the theory of the devices, but with the theory of the semiconductor material itself, because a semiconductor material would match the theory only if it were defect-free, and no such materials were available before WWII.

Before having such crystals, making semiconductor devices was non-reproducible, you could never make two that behaved the same.

"FETs work by bending the energy levels of the conduction band" is something used in textbooks, together with some intuitive graphs, with the hope that this is more intelligible for students.

I do not think that it is a useful metaphor. In any case this is not how you compute a MOSFET. For that you use carrier generation rates, carrier recombination rates, carrier flow and accumulation equations.

Instead of mumbo-jumbo about "band bending", it is much simpler to understand that a MOSFET is controlled by the electric charge that is stored on the metal side of the oxide insulator. That charge must be neutralized by an identical amount of charge of opposite sign on the semiconductor side of the gate. Depending on the sign and magnitude of that electric charge, it will be obtained by various combinations between the electric charges of electrons, holes and ionized impurities, which are determined by a balance between generation and recombination of electron-hole pairs and transport of electrons and holes to/from adjacent regions.

All the constraints lead to a unique solution for the concentrations of holes and electrons on the semiconductor side of the gate, which may be higher or lower than when there is no charge on the gate, and which may have the same sign or an opposite sign in comparison with the case when there is no net charge on the gate. This change in the carrier concentrations can be expressed as a "band bending", but this, i.e. the use of some fictitious potentials, does not provide any advantage instead of always thinking in carrier concentrations. (The use of some fictitious potentials instead of carrier concentrations had a small advantage in computations done with pen and paper, but they have no advantage when a computer is used. The so-called "Fermi level" is not needed anywhere, it just corresponds to the rate of thermal generation of electron-hole pairs, which is what is needed.)