If you wanted to scan bi-directionally as you suggested, the speed of the beam going left-to-right would have to be exactly the same as the speed going right-to-left, and it would have to be exactly the same speed over the whole width of the scan. If it did not you would get misalignment of alternate lines, which would look terrible.
This means the electronics controlling the horizontal scan coils would have to generate a very symmetrical linear triangle wave. With modern electronics that's trivially easy to do, but TV began back in the days of vacuum tubes (valves). Generating a linear triangle wave would have been possible but would have increased the component count and the size and cost of the set.
With the scanning setup that was used you need a sawtooth waveform, but it doesn't have to be very linear. Any non-linearity will show up as compression of the picture over to one side of the screen, but for most TV images that's acceptable because it's not very noticeable.
Secondly, the way you describe the scanning process is not totally correct. The beam does not move down the screen only during the flyback, it moves down the screen continuously, because the vertical scan is also driven by a sawtooth waveform. Each line on the screen is slightly slanted, but again that's not noticeable to the viewer.
Now imagine if you were alternating left-to-right / right-to-left. The lines at the edges would overlap each other and there would be gaps between them.
It is probably to do with the technology of the time when standards were defined. This was probably a step too far, adding extra vacuum tubes and complexity in a device that already had a lot of them.
Larger CRTs as for television tended to require magnetic deflection, so inductors are involved, because it needs excessive voltage to get the required electrostatic deflection.
The point is that to generate a triangular scan waveform the current in the inductor of the scan coils needs to be ramped up and ramped down in a triangular fashion. The driver could be a voltage or current source amplifier in linear mode, with more complexity, power dissipation and such. If the driver is a switch instead (using a rectangular wave voltage to turn it on and off at appropriate times), the resulting current wave form and scan is not a triangle but a sawtooth. This is because the current change is sudden when switched off. It is not so simple as this, but for an explanation, that is enough.
Another advantage of the fast horizontal fly-back is that it can be used to generate the eht for the crt anode supply by adding a high voltage winding to the deflection transformer. If the current rises linearly and then falls linearly (triangle), the voltage is much lower, and probably a separate EHT power supply would be needed. There is a limit to the step up obtainable by turns ratio of a transformer alone. Using the fast fly back, a very high voltage pulse appears in the primary to be stepped up in the secondary.
The deflection coil and fly back transformers are inductive. They are driven by a single vacuum tube or transistor. While the transistor conducts the flux builds slowly and the beam scans across slowly. Then the transistor is turned off which causes a huge voltage spike on the transformer and coil that discharges the transformer flux quickly and retraces quickly. When ever you try to stop the current in an inductor it fights back with a huge voltage "fly-back". A "damper" diode is required to limit the voltage spike. To retrace slowly, you would need more transistors to deliver a reverse voltage. It would also complicate the video signal. BTW the trace is constantly moving down. The lines are actually ramps but then you just twist the deflection coil to level them out. In any case this is ancient history so you should be studying LCDs instead.
charcinders provides an excellent answer - but one more aspect you might consider is the inertia you mention - it also applies to the electrical power bringing the beam to a stop and reversing it in your plan - instead of occurring during the retrace time, there would have to be an allowance for the time it takes the electrical field to collapse and build in the opposite phase. Reasons given are much more valid because the timing of reversal would be even messier.
There are many ways to do it. When it was designed in ~1930 this is the way they picked because of what they knew and the tools they had to work with at that time. It became the standard and everything after that was designed to fit the existing standard.
It is difficult to reinvent the wheel, while it is on a loaded truck rolling down the highway.
Yours is a good idea but will never happen now that there is HDTV.
The dual-scan method is used in TELEVISION to produce a picture with greater visual acuity. If you used the sequential scan method, there would be small black line between each scan of the beam,making the picture look really crappy.
at the end of first line , beam instantly returns to the left...vertical field pulls it a little down and horizontal field starts sweeping.......
horizontal and vertical oscillators use sync pulses from video signal.....means ....the first point on left top on camera ( or video signal ) and tv receiver start simultaneous ...also jump to first point at the end of frame....
on camera picture transmitted line by line ....from left to right....
if sweep starts from right ,the phase of hor. oscillator should be changed so needed additional circuit to distinguish its phase,,,
In raster scan when the beam reaches the right-hand side of the screen it undergoes a process known as horizontal flyback, in which its intensity is reduced and it is caused to "fly back" across the screen (the top-most mauve line). While the beam is flying back, it is also pulled a little way down the screen.
Because of the inductive inertia of the magnetic coils which deflect the electron beam, there is a delay named horizontal/vertical retrace time.
*** Why the beam does not scan even-numbered lines from right to left (like below image)????
Horizontal retrace(flyback) time can reduced. There is no need to deflect beam horizontally at end of each line. just a tiny vertical deflect needed.
