Syncing directly from a 4G signal would be a lot more practical than VLF or HF time signals, but I haven't found a wall clock that does so.

On the one hand, yes. On the other, my country has just shut down 3G and 2G only stays because it's still used by emergency services. How long will 4G last? Longer than bluetooth and the Casio app?

It'd be nice if something like this could be maintained long term. The US, UK and Germany signals have been working since the ~1960s.