Your objection is flawed. A single bitcoin is enough to host all the trade in the world. Let me expand just a little bit on that statement. If, hypothetically speaking, Satoshi had programmed an upper limit of 1 bitcoin instead of 21 million bitcoins, it would not have made any difference on how the whole thing functions. The total valuation of all circulating bitcoins in existence expands or contracts to whatever it needs to be. I suggest you ponder the basic idea of a unit of measurement and what it means to change units.

If you want to study the history of currency and banking, you should read about the history of economies that have run on privately-issued currencies without any government-issued currency at all. This is referred to as "free banking." Scotland had a pretty long run in the early 1800s (iirc) of free banking. My point is that currency does not necessarily imply formalized government-issue or government-backing.