For it to be general, I should be allowed to do everything I can do with a PC, without any kind of constraints or workarounds.
Exactly because most people pay more than $300 for an unconstrained device, there is little value to pay more than that for a constrained device.
A smartphone is definitely a general purpose computer, though. The definition of a general purpose computer isn't "a computer that can do anything a typical PC can".
A proper definition would be something like "Any computer-based device that accepts different applications". It's a differentiator between things like microwaves, which are technically computers, and smartphones/laptops/PCs/tablets.
Mobile OSes are special purpose, constrained to their phone + apps, developed by on external devices.
Being able to develop software for a device on that device also isn't the definition of a general purpose computer.
A general purpose computer is one that can be easily made to run different programs. Again, it's a differentiation between devices like microwaves and ovens that are technically computers, but aren't used like computers by the general public.
I guess I will prepare that accounting document with a Bluetooth keyboard paired with my fridge.