1946 Why 405 lines?
I recall being told way back when I was being taught television system fundamentals that, whilst the flicker reduction was the 'headline' or 'PR' reason given, the analogue compression with its halving of bandwidth was the real win and a very substantial contribution to achieving good resolution over a complete system when, as has been said, stretching the bandwidth with the valves and technology of the time was a real headache.
It's anecdotal, but I'd heard that the EMI engineers were at last mastering the techniques necessary for the frequency response needed for 243 lines when Schoenberg decided that he wanted something that would decisively outclass Baird's 240 line system as opposed to merely equalling it, hence the replacement of 3x3x3x3x3 by 3x3x3x3x5- apparently a simple step, but in reality for the EMI engineers a bit like saying "Well done on completing the marathon- now we want you to do it again".
Talking of bandwidth kludges, Kell factor also seems like a handy outcome of a brainstorming session- "Come on now, folks, a raise for anyone who can nibble a bit more off the upper frequency limit- we'll come up with a justification somehow...."
A sequential 405 line system will have a line frequency of 20,250c.p.s. so the active video will be slightly less than 50 microseconds and the bandwidth will be four times that of the interlaced system of the same number of lines. In fact the sequential system will not have an odd number of lines, it would be something like a 404 or 406 line system.
The French 819 line system E required a video bandwidth of 10Mc/s to realise it's full potential. Never seen it but I'm told the picture quality displayed by the Belgium 819 line system F squeezed into a VHF system B channel was not good. Horizontal definition was awful. 405 looked better.
If there had been LCD displays back in the 405 line era the questions of flicker would not have arisen and the Baird 240 line offering might have been more attractive except that the Baird company had no viable camera.
Who would be up for the mathematical challenge? - Just supposing we increased the lines by tenfold? Let's make a virtual 4'050 line system. Let's keep it analogue, let's keep it B&W, and let's assume that we would be using modern solid state devices to achieve a result.
Would anyone care/dare to throw some numbers into the ring?
Well if we use a bandwidth of 3MHz with 405/50 interlaced then for 4050/50 interlaced we would get the same horizontal resolution with 30MHz but if we wanted to have the 10x resolution horizontally then 300MHz bandwidth would be required.