Why is the Deflection and High Voltage Combined?
One of the main reasons that TVs and many monitors are designed with horizontal deflection driven flybacks is simply economics – it provides a cheap way to get the high voltage and many or most of the other voltages for the set with minimal hardware. (High quality computer monitors sometimes use a separate high voltage supply so that the horizontal deflection is then used just for deflection to reduce interactions between changing scan rates and the HV.) A side benefit is that if the horizontal deflection dies, the power supply voltage goe with it and prevents the CRT phosphors from burning do to undeflected high intensity beam. The use of the horizontal frequency rather than the AC line frequency of 50 or 60 Hz allows the power supply components to be small and light compared to a line operated power transformer and filter capacitors.