There's a middle ground between locally installed software that fails as soon as you don't have an internet connection for the phone home, and locally installed software that can be used totally unplugged. You can stick a countdown timer within the software that allows 7, 30, 90 etc days of consecutive offline interactivity before the user needs to phone home again. Heck, if you really wanted to, you could sell copies or subscriptions to that software at varying price points depending on how many days the user expects to need - if it's a feature people want, it's a feature you can price in.
Why isn't this model more common? Mm, plenty of reasons. You need to implement pretty sophisticated techniques under the hood to deter software crackers, for one, which aren't required when you make an API call every sixty seconds to an Azure Function. For two the modal human mind really hates middle grounds of this sort. I actually suspect that some "online-only" local software implements something like this under the hood, and just doesn't advertise it, or perhaps gates it being being an enterprise feature. (I have unfortunately learned firsthand that advertising my software as "works up to 30 days off-grid" gets considerably more ire than "ah, sorry, it does require an internet connection, everything's in the cloud these days, you know how it is".)
But probably the most common reason is simply that most people don't need it! Most regular people aren't using software at all when they go off grid.