I don't think so. In a hypothetical future where bitcoin becomes a globally used currency it could, but it is very hypothetical and there are too many drawbacks to reach that future such as scalability, ease of payment with other alternatives and that it is increasingly used as a store of value.
You're right. Even if hypothetically it does become a globally used currency, we still also have to rule out a certain percentage of the globe that won't use it. There are nations where electricity is a huge problem. Nations like that will have a hard time assessing Bitcoin. Again, that something is globally recognized doesn't mean everyone will use it. Take for instance, the US dollar is a global currency but not every nation of the world use it.
On Bitcoin eliminating banks, I'm of the opinion that won't happen. Even those who use Bitcoin in most cases will convert it to fiat before spending it. How do you get fiat if not through banks?