Agree with your points. Also, your comment reminded me that habitable, unhabitable, inhabitable, uninhabitable, is one of the most confusing situations in the english language.
There's no reason why it shouldn't, though. It makes logical sense.
(to be fair, by this definition, unhabitable is in fact a word)
Yes, though "habitable" is the normal word and "inhabitable" would be a nonce construction derived from "inhabit".
> It's like[] inflammable and flammable.
Not really; those words mean that something can catch fire. That's all well and good for "flammable", but it's bizarre for "inflammable", since "inflame" has no surviving meaning related to fire. If you wanted to express that meaning, you'd have to say "set fire" or "ignite".
The joys of english.