I'm not going to validate the idea that you can change the true character of something simply by putting artificial restrictions on its use.
First off, it's not just artificial restrictions as I outlined earlier - there are indeed technical limitations inherent in the platform. These may be largely eliminated with the next gen, but we're not there yet.
Secondly, it's not an "idea", it's reality. There's a reason there's no word processors for consoles currently - they can't run them. Arguing that it may be technically possible is irrelevant to their actual utility, that utility defines the device.
Basically by your logic, the term "PC" can mean anything with a CPU that could potentially run code. Therefore:
Your microwave is now a PC.
Your Tom Tom navigator is now a PC.
Your digital thermometer is a PC.
Your arbitrary definition of the term leads to it becoming meaningless. You're arguing that there was never a need for the word console; there was - hence it was created and used for the past several decades to describe a certain class of device.