because it is the theoretical impedance for a 1/2-wave center-fed antenna (73 ).
An ideal a 1/2 wave center-feed dipole antenna in free space have an impedance around 83 Ohm.
Antenna impedance is a complex value consisting of antenna resistance and reactance.
By making a dipole antenna shorter then 0.5 lambda can reactance part be compensated for. Typical 0.47 lambda and reactance is very low and antenna resistance have dropped to around 65 Ohm. A possible problem is that matching coaxial cables at 65 Ohm are rare.
For TV-reception will that mismatch make minimal difference but if transmitting several kW and a such mismatch can start a fire.
It can in any case be seen that a dipole antenna impedance is not something that did decided coaxial cable impedance for some kind of natural impedance matching.
Cable characteristic impedance (resistance when reactance i zero) is selected depending on what cable properties are preferred for each situation, however are 33 and 75 Ohm two optimal values using air-filled coaxial cable (max voltage and min loss).
It is mostly when low losses are of high value that air-filled coaxial cable is used today due to cost and these cables are designed solid or semi solid.
If replacing air with something else must its dielectric properties be taken in account which affects cable impedance and velocity factor.
There are many stories why 50 Ohm and not something else. Probably are many of these stories correct and part of the history.
17, 33, 51.5, 60, 75 and 93 Ohm have all been used or is in use as coaxial cable impedance because specific advantages. A bit fun equipment designed for 51.5 Ohm coaxial cable is
this BIRD restive load.
In Europe was 60 Ohm a common impedance in European military radios during WWII and US military selected 50 Ohm. Quality transmission lines was a new need due to relative powerful transmitters was developed in a never before seen numbers why rigid 50 Ohm coaxial cables (steel tubes) was developed.
It was not practical to use ladder line inside airplanes, tanks, ships and submarines (was more common during WWI).
Steel tubes was also very reliable kind of cables, survives rough handling, even fireproof and can be bolted directly at other steel structures so it fitted military needs very well.
Hewlett Packard did became a mayor player for measurement of radios a few years after WWII and they offered only instrument with 50 impedance as US military was its greatest customer.
European military had no choice, they switched from 60 to 50 Ohm due to practical measurement reasons.
Same numbers as 50/60 Hz.
55 Hz is maybe a diplomatic halfway switch from both sides
.
When TV at higher frequencies did became popular did HP add 75 Ohm alternative for its measurement instruments as low loss impedances was more important for TV reception then transmitting a lot of power and TV and broadcast FM radio seemed to be a big thing.
For that was a flexible coaxial cable needed between radio and antenna as well for cable TV. Fixed steel tubing is way to expensive and it would become unpractical to move around a TV if connected with steel tubes. Have to call a plumber to move around the coaxial cable.
Selected cable was instead a more flexible type, a foam filled cable with properties very similar to air-filled cable as the foam mostly contained air.This cable did replace older antenna cables for TV-set, typical a 300 Ohm twin lead.
Table FM radio was born during same period but there did twin lead cable survive for very long time as at 100 MHz are twin lead cable losses not as high as for UHF (>300 MHZ).