Keep in mind that central banks existed when there was a gold standard. There is no reason there couldn't be a lender of last resort on a Bitcoin standard. However, as your wrote, since the banks are backed by reserves (instead of a printing press), the reserve requirement could not be as low as it is now.
Yes, a "Bitcoin Central Bank" would be basically a bank like every other. In theory, one could imagine a state-backed Central Bank even in a society with a Bitcoin standard. Such an instituion could give out Bitcoin-pegged, state-backed stablecoins in times they want to increase supply. A kind of "Government Tether", basically a bond with "character of money". This approach has been used in countries like Argentina (the infamous "Lecop") already, with some (limited) success, although obviously not with Bitcoin but the US dollar as standard.
However this approach would be limited if the Bitcoin price had still a tendency to go up, due to the risk of a state insolvency. It would not be suited for the "Venezuela scenario" I had in mind, but perhaps in the long term when Bitcoin reached a relatively stable price after a period of mass adoption.
I don't think it would result in a credit crunch since the value of the money would increase until the supply is sufficient to meet demand.
I don't understand fully what you mean here. Just the phase with increasing money value would be the one where access to credit would be severely limited.
Second layer may be a solution to this problem, and one of the scenarios that can do this is this project --->
https://github.com/omnilaboratory/OmniBOLT-spec.
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This feature will provide the possibility of lending in BTC/ALT/stablecoins, such as USDT, and Bitcoin can act as a partial reserve system.
True, technical solutions like Omnibolt can definitively help. A partial reserve system based on these tools is surely interesting.
What however could be a problem (if my interpretation is right) is the total transparency: Let's say a Bitcoin bank issues partially backed stablecoins. If the level of the reserve goes down because the bank tries to increase liquidity, this would be visible for everybody, and this could unleash a domino effect of sinking trust in this bank and problems to maintain the Bitcoin peg.
One possible idea is to combine the Bitcoin peg with a commodity-based peg. Banks could invest in "real-life" commodities and use these investments to back their Bitcoin-based stablecoin partially.
@extasie: Pretty much this. It would be a systemic fault. While an excessive credit liquidity is also not good, the crunch imo would exceed greatly a "sane" reduction of that liquidity.