For better or worse, that is the inherent assumption - that a smartwatch is a companion device to a smartphone. The idea of ditching the phone entirely is, arguably, an unintended consequence of releasing smartwatch variants with built-in LTE connectivity. Giving the app developers the benefit of doubt, it's understandable they don't want to make a standalone app for a fraction off the smartwatch models, where they can do with one simpler extension app for all smartwatches.
There is nothing inherent in the hardware limiting you from doing these things, but my understanding is that Apple makes it hard to do.