Imagine you wanted to start a bank, so you create a cooperation and issue 1 million shares of stock to the shareholders. On the date the bank is formed, it has no capital.
What is the face value of every share?
That question seems to me to hide quite a can of worms.
I'm more interested in rather practical questions. What is the nominal value of each share? In what currency and how is initial capital paid in?
There is no nominal value, they start out valued just like bitcoins did. Someone decides to place a value on the company. A share is just a percentage of the market assessment of the value.
With regard to why would someone Borrow a USD Note from the bank... because they could sell the USD Note for real USD to someone who wanted to make a deposit into the bank. So while it may appear that it was a game of musical chairs, in reality it enabled decentralized deposit and withdraw of real USD by exchanging USD Notes of the corporation for real goods and services.