I believe other systems send data constantly in real time. As loose rivets said, in this day & age I can have a simulated motor race in real time with a teenager in Tokyo, so we really shouldn't be dependant on fishing bits of orange metal from 35m depth in the Med to know what has happened.
The challenge here is that airplanes in the sky have such a big "radio footprint" i.e. the transmissions carry far away, which means re-use of the same frequency is only possible far away. This means you quickly would need a lot of frequencies. In contrast, land-based cellular systems can re-use their frequencies every few kilometer or so, which means thay have much larger capacity to handle many continuous data streams.
One possible solution is to use self-organizing multiplexing techniques to share a few frequencies in an intelligent way. There are techniques such as STDMA (Self-Organizing Time Division Multiple Access, used in VDL (VHF Data Link) Mode 4 for ADS-B) and CSMA/CD (carrier sense multiple access with collision detection, the basis of how Ethernet works but not directly suitable for aviation radio).