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There is a hard line between insolvency and illiquidity. Illiquidity can be solved by borrowing at the federal funds rate.

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I kinda agree here, it's a cash flow question. But that doesn't resolve what the haircut (if any) should be put on the securities in question nor what their future value will be.

The BTFP does it for one year without a haircut. Is it long enough? Depends on where long term rates go. If they fall a couple of points in the next year, it could, but if the Fed fails to beat inflation and they rise... then it wouldn't.

The other problem with BTFP is that it makes less HQLA collateral available in the swaps market for securities with similar tenors to those locked in BTFP. In one hand you increase liquidity for the most liquid assets on bank books, and on the other hand you decrease liquidity for least liquid assets on bank books (and private holders of said securities, private $ denom debt > us gov debt).

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