To send a fax you need access to a handhshaked landline. A direct wire between the stations. Faxes synchronize themselves, send data and test the bit, makeing sure it is properlt placed in the data queue, and send the next and so on =handshake. Suggest you look up old fax synchronization and I tossed my last muirhead rotary in 1982 - used it for weather maps. https://electronics.howstuffworks.com/gadgets/fax/history-…
What exactly makes this "hard via radio"?
There are radio-fax standards. Marine weather reports are a good example that's still in use: https://en.wikipedia.org/wiki/Radiofax
However, the fax machines we use on our telephones were not designed with this in mind. The protocol is neither tolerant of the reduced bandwidth nor lossy compression from cellular networks... not to mention jitter if the call passes over a packet-switched network.