Why can’t I set my iPhone like a radio alarm clock,

Apparently iPhones have a theoretical capability in that their chip that handles wireless communications is objectively capable of processing FM signal, but that function has never been implemented and in any case you’d then need a tuner feeding into the processor and an aerial feeding into the tuner, and those were never in the iPhone. iPod Nanos after a certain generation did have an FM tuner but it only worked if wired headphones were plugged in since those would be the aerial. Source: Is there an FM Receiver in an iPhone? - Apple Community

As mentioned, “radio stations” on an iPhone are really apps that stream the station(s) programming over cellular data or WiFi. As I read the page linked in the OP, I am under the impression the experience does not truly emulate a radio clock, where the sound of the live programming IS the “alarm”, but rather it’s an automation that launches your radio app when you hit snooze.