In short, whenever you can’t or don’t want to use the internet for the comm link between the base and rover. It’s just simpler to not use the internet, fewer moving parts. And you might not have internet access. Or you might not want to bother getting the internet comm working. But an internet comm link does have advantages - no radio interference, communication over longer distances, etc. I do most of my RTK work where there is no cell service or internet access, so I use telemetry radios.
There are many ways to achieve RTK.
They all involve a rover GPS/GNSS receiver measuring coordinates of points of interest while receiving raw GPS observation data in RTCM format or similar from a base. (Sometimes people call this data stream ‘correction data’ but it technically is not, despite what the SparkFun documents call it.)
They all involve some type of base GPS/GNSS receiver at a known or assumed position, transmitting its raw GPS observations in RTCM format or similar.
They all involve some type of comm link between the base and rover.
The rover uses its own GPS/GNSS observation data and the stream of received observation data from the base to calculate a very accurate relative vector between the base and the rover. And with the coordinates of the base and that vector, the rover can calculate the coordinates of its location.
There are many options for the comm link.
One is to connect both the base and rover to the internet, and transmit the data from the base to the rover over the internet. But of course you need internet access at both locations, which isn’t always possible or practical. And of course when you connect two devices to the internet, they need some way of connecting to each other, which generally involves the base having a fixed ip address, or using a third server (or service) to allow them to make a connection.
Another is to use radio modems to transmit the data from the base to the rover. Telemetry radios are radio modems. This is useful if you’re working out in the woods and there is no WiFi or cell service. It is also conceptually simpler - setup the base, turn it on. Turn on the rover. Go. No need to connect to the internet, etc.
You could use even use a cable, though you couldn’t move very far.
You can even log both the rover and base observations to a file, and later post process the data to find the location of the rover. But that’s not Real Time Kinematic, it’s Post Processed Kinematic.