After hyperbitcoinization the value of bitcoin will reach something like steady state, dictated only by population, demand for debt, and world-product. Possibly something on the order of world-wide M3 fiat along with other stable but non-interest and non-dividend bearing assets. This number could be anywhere from a half quadrillion to 30 quadrillion (rough order of magnitude). This puts bitcoin somewhere between $0.25/sat to $15/sat of today's money.

We have some evidence of what a closed economy looks like with a steady state hard money supply. Steady-state only needs to occur for a short period of a few years to see what that might look like.

What tends to happen is a lending currency is established by lending banks. The lending banks use their customer deposit reserves to issue debt certificates to lenders, and the lender will spend the redeemable notes into the economy in lieu of the actual hard-money. Of course eventually there will be a run on a bank if it is found to not be able to meet its demand-deposit draw for reserves of the hard currency. This event is used for the fear-mongering that leads the shortsighted to demand a central bank (lender of last resort).

The reason banks issue demand deposit notes rather than lend out the actual hard money is people tend to not want to carry around the actual hard currency for fear of theft. The feature of banks allowing a depositor to write cheques allows the bank to provide the service of security and withdraw certification in exchange for being able to underwrite debt and potentially render interest to the depositors for access to the reserves.

Bitcoin will not change this need to issue credit, unfortunately Bitcoin does not fix this. With the transparency afforded by low-friction communication and complex bitcoin wallet executable contracts, the likelihood that a debtor will want to loan a bitcoin-backed and bank-issued coin is low though not impossible. The debtor would likely have difficulty spending those coins into circulation. The alternative is to issue bitcoin securities that are redeemable for bitcoin, something like wrapped bitcoin, but the issuing lender may be able to fractionalize the reserves and provides some kind of electronic contract enforced assurance in combination with depositor insurance that the coin holder will be able to eventually settle in bitcoin.

An alternative to the fractional reserve scheme to resolve the need to issue debt is the certificate of deposit backed by partial insurance. The interest rate would need to be high enough to cover collection, lawsuit and insurance costs, yet leave enough interest to encourage reserves holders to sign onto such deposit agreements.

The need for all this bitcoin based lending will most likely never materialize so long as a relatively stable fiat currency continues be accepted in commerce.