That's not how banks work. Banks are factories not warehouses.
Banks create money out of thin air. The loan comes first and that causes the deposit - which is then trapped within the banking system for that denomination until it is used to discharge a bank or government liability in that denomination.
As the Bank of England explains: http://www.bankofengland.co.uk/publications/Documents/quarte...
The ability of banks to leverage deposits into fractional debt is restricted by the size of their deposit base and the need for fiat assets to earn competitive rates of return. This is not a "one way street".
Once people start shifting capital to crypto, banks will sell assets to cover withdrawals, and the cycle to which you refer starts to spin in reverse as the worsening terms-of-trade for fiat/crypto exchanges triggers a fall in the real value of assets in terms of fiat. In short, we are going to get more inflation as crypto spreads because there is less stuff being sold for fiat and more stuff being sold for crypto or held because people don't want to trade it for something likely to lose value.
At that point banks will have to raise interest rates to ensure they are not lending at a loss. Higher rates will weaken borrowing and push more borrowers into bankruptcy, at which point your expansionary cycle reverses until enough loans are written-off and the debt overhang is reduced and/or inflation eats up the implicit increase in the money supply relative to actual underlying GDP.
I always posit this question, to which I have never received a satisfactory answer: What, exactly, would the US do if the world suddenly decided that the dollar was worth nothing?
Massive buybacks of dollars by the Fed would be seen as an ineffective and desperate move. Besides that, what other recourse do they have?
If the influx of USD was higher and faster than could be addressed, the economy would naturally get inflation that would force interest rates even higher up (since no banks will lend at a loss, so borrowing costs get pushed up first by the fed, and then by the need to cover for expected inflation). This would be a death blow to many indebted and highly-leveraged businesses that are dependent on low interest rates for operational purposes (including those in the financial sector) and so they would go out of business. The need for the financial system to write-off the debt held by these companies would also eliminate a certain amount of money in circulation. Eventually enough money has been destroyed/absorbed and the economy is back in equilibrium.
On a less than academic note: this is not a totally unlikely scenario since the flight-to-crypto is a de facto process of de-dollarization, with crypto assets essentially replacing fiat both as store of value as well as medium of exchange. Put another way, the increase in the value of cryptocurrencies is really just a loss in the purchasing power of everyone holding fiat, and since these additional assets are now competing to purchase the same pool of goods, what people think of as bubbles in assets like housing are really just reflective of inflation in the underlying supply of money-that-can-buy-things. And it will get worse when you can sell your house for crypto.