How does a CRT television flyback really operate
Your schematic is missing one of the most important components, which is the horizontal deflection yoke/coil (that is mounted on the neck of the CRT) which is in parallel with the primary winding of the transformer.

Most of the energy exchange during an horizontal cycle, including the resonant flyback pulse, is with the horizontal yoke (not the flyback transformer). Only a small fraction of the energy goes through the flyback transformer. Some of the energy is siphoned off through the flyback transformer during the flyback pulse to generate the high voltages.


The horizontal voltage in combination with the inductance of the horizontal yoke determines the current ramp that is required to deflect the electron beam from the left edge to right within the prescribed horizontal period. That voltage can be 12 to 15V for a small 12" CRT with a small yoke or it would be higher for a large CRT, so it is not necessarily 150V.
From what I have seen, I would guess that most if not all raster CRT horizontal deflection circuits employ this resonant flyback scheme. (Obviously, a vector CRT display, like in an analog oscilloscope, would be different.)
Here is a good app note on the CRT horizontal deflection circuit:
https://www.fairchildsemi.com/application-notes/AN/AN-9009.pdf