You're definitely missing something, because private lenders are perfectly free to charge interest. ZIRP applies only to federal debt.
"Yet, why would I, as a banker, lend to the government at all?"
Currency issuers never need to borrow. That is an incorrect statement of why Federal debt exists. Federal debt is a savings instrument, and as Europe and other negative interest rate debt has shown, there is still a market for savings instruments even at the zero lower bound.
https://www.bloomberg.com/news/articles/2019-08-15/negative-...
"Negative-Yielding Debt Hits Record $16 Trillion on Curve Fright"