This is not a historical answer, just an observation.
A lot of'strange' frequencies come from the tv industry, where they are multiples of 60 Hz and/or 50 Hz and the scan frequencies. Some of the others, around 1.8 mHz were used for time-keeping and baud rate generation.
All of the baudrate clocks are multiples of 16 times the base baud rate becuase all the serial ports used 16x clocks to capture the edges.
I think the 14.3 mHz is 4x the color burst frequency of 3.58 mHz. I don't know where the 3.58 or the 525 lines came from, so this may simply be pushing the question back another level. Probably had something to do with which side of the road the Romans rode their horses on.
The early computers had the processor and the display frequencies synchronized, both for practical reasons and because the crystals were dirt cheap, and we were dirt poor.
It took me a while as a designer to break away from 'standard' frequencies and begin ordering crystals that were exactly what we needed in our industry. Again a bunch of non-integer values, but chosen to provide integer relations among things that were releveant.
DspDad