Just a couple of random thoughts here:
First, what about television and FM radio signals that rely on line of sight (as opposed to AM and shortwave signals that travel far longer distances)? Just speaking about TV signals (with which I have far more experience, I've been a hobbyist for over 50 years), given a totally flat surface (i.e., with no hills or mountains between you and the TV transmitter), the signal normally peters out after about 75-80 miles. (I won't complicate the scenario with "knife-edge propagation", where the signal hits a mountain ridge or similar obstruction and glances off the top, with enhanced reception on the far side of the ridge --- that can enhance coverage areas considerably, and in the mountains, TV signals can do bizarre things. Very often, what cities you get TV stations from depends on what side of the mountain you live on, and TV signals also "snake" down valleys and similar features.) TV towers are no more than 2000' tall, lower if they are on a high mountain, as the FCC wouldn't tolerate a 2000' tower on top of a 5000' mountain. If the earth would flat, that signal would go on forever, or at least until it were dissipated so as to be too weak for reception. Yet it doesn't do that. Here's an example of an idealized situation, where the signal goes out over water (I used WSVN channel 9 Miami, to show a signal that largely goes over either water or pancake-flat terrain, the tower is 1014 feet tall at sea level):

Notice that the signal abruptly stops about 60-80 miles out (I imagine they truncate it so as not to waste signal over the ocean where there are no viewers, also, the signal is directionalized north-south, presumably for similar reasons, whereas most of the time, TV signals are omnidirectional). Granted, out at the edges, the signal is weaker (the area shaded in light red), but it reaches a certain point, and >POOF!<, no signal at all.
Second, what about microwave signals? Unlike conventional TV signals, they are laser-precise, used to get a signal straight from one point to another. The first example that comes to mind is WHIS-TV in Bluefield, West Virginia (now WVVA), which had to get a microwave signal from Roanoke, some 70 miles distant (the following is snipped from
https://jeff560.tripod.com/whis2.html), to be able to offer network programming which didn't get all the way to Bluefield:
How was the new station to supply sufficient programming to justify its existence? Network was the obvious answer. But, as usual, there was a hitch. There were no network common carrier facilities, and when approached on the subject, the American Telephone & Telegraph Company indicated it had no plans to put in common carrier connections between Bluefield and Roanoke, the closest city receiving network television signals.With typical resourcefulness and determination, Jim and Hugh Shott (by now president and general manager, respectively) decided to build their own microwave relay system to bring NBC programs from Roanoke, a distance of some 70 air miles. RCA, pioneer in broadcast electronics, agreed that such a theory was sound, but had never been attempted over such terrain nor for such distances. They accepted the challenge of creating necessary equipment, but Pat Flanagan was handed the awesome assignment of planning, installing and operating the system, an entirely new and unusual job!Pat poured over U. S. geodetic maps tediously selecting and rejecting routes and sites for relay transmitters and receivers. Eventually they settled on the first relay receiver and transmitter 13 miles west of there to a spot appropriately named Dismal Peak; and from there to the top of East River Mountain. It looked good on the map. Getting men and equipment up the rattlesnake infested, rocky mountainsides was something else! Equipped with compass, binoculars, searchlights, mirrors and snake-bite kits, Pat and his boys set out.First, they leased space at station WDBJ to house equipment to pick up and transmit the network signals from AT&T. Then the direct line-of-sight path (the only way microwave can travel) from Roanoke to Poor Mountain was established by a man standing on top of the Mountain State and Trust Building in Roanoke reflecting sunlight with a mirror so that another man on the 13-mile distant Poor Mountain could pinpoint the originating location. This process was then repeated from that site to Dismal Peak and again to East River Mountain.Microwave travels much as a beam of light travels. The transmitting antenna "dish" projects them as an automobile headlight reflector projects its beam of light. The pattern is slightly conical, like the beam from a powerful searchlight, four feet in diameter at the originating point. It loses power as it travels, and when picked up at the next relay point the signals brought up to full power and re-transmitted to the next point. All this by air! There are no physical wire connections. The same microwave relay system COULD carry not only television, but telephone, telegraph, radio and very likely will one day replace the maze of wires and telephone poles now dotting the horizon.Sound and picture travel together, although they are actually two separate signals. The sound, or audio signal, is an FM (frequency modulation) radio wave. That is why Channel 6 television sound can be picked up on FM radio. The picture, or video signal, is an AM (amplitude modulation) radio wave. The two are combined into a composite beam by a diplexer at the transmitter in Roanoke, and unscrambled when the beam reaches the transmitter on East River Mountain.If all this sound complicated, it is! To get the first equipment up the mountains and operating, point to point, voice circuits were established through telephone switchboards at towns along the way, so Pat and his boys could talk back and forth while attempting to establish their line-of-sight paths.The towers at each relay point, designed by Flanagan and still in use, are four 50-foot creosoted telephone poles, with a large platform built on top to support antennas and external equipment and also allow room for men to service them. Ground equipment at the relay points is housed in prefab steel houses, and is remotely controlled. When the network comes on in Roanoke, it automatically starts the transmitter, which by a signal starts the next.The WHIS-TV microwave relay system is one of the very few privately owned systems in the country. Even today, RCA (who built the equipment for a mere $70,000) brings its research and development engineer-trainees to WHIS to study the system. Meanwhile, back at the Municipal Building excitement was mounting as Pat assured his staff that completion of the microwave system was nearing.On September 26, 1955, the Herculean task was done. At 4:00 p. m. the "Pinky Lee Show" became Channel 6's first network program. I have to think that all of this Rube Goldberg-like rigamarole presupposed a curved earth, not a flat one.