So long as the bank does not make too many bad loans

that is a big IF

The entire bank crash issue in 2007-2008 was a direct result of intentionally made bad loans.

The U.S. Senate's Levin–Coburn Report concluded that the crisis was the result of "high risk, complex financial products; undisclosed conflicts of interest; the failure of regulators, the credit rating agencies, and the market itself to rein in the excesses of Wall Street.
https://en.wikipedia.org/wiki/Financial_crisis_of_2007%E2%80%9308

Congressmen wrote a law that "made" the banks give out ridiculously bad loans, with the foreknowledge that the taxpayers would take the risk. The banks bundled up these bad loans and used them as a commodity, again knowing they were taking no risk.

So the taxpayers bailed out some of the banks, and the congressmen got their baksheesh

fractional reserve banking is fraudulent in practice because banks don't disclose what they do with deposits

which is what exactly what happened

as long as the banks are underwritten by the taxpayer, the taxpayer has the fiduciary right to see every last cent on the account sheet.

In effect, I agree with you. It is not the banking system in itself that is a problem; It is the behavior of those in charge of the banks, and the politicians that allow those in charge of the banks to sandbag their own balance sheets for a taxpayer-funded profit.

Two immediately apparent fixes that should apply

• First, all banks that are protected by taxpayer money must be fully transparent. If they want to make profit by taking confidential risks, they should move into the investment field, not the banking field.
• Second, enact the death penalty for any public theft of more than 1 million dollars. The penalty would apply both to the banker that made intentionally bad loans, and to the politicians that facilitate such thievery with joke laws like the CRA