Deposit insurance is unhelpful to the state

It is the central bank which enables the commercial banks to attach their credit to that of the state. Via deposit insurance the broad money issued by the commercial banks is given the same value as that of the base money irrespective of the credit-worthiness of the banks. The banks are able to get into as much debt as they like and in contrast to the state they have little interest in protecting the currency. The state (we must assume) has an interest in preventing inflation because this could have a negative impact on the voters but the banks have no such concerns. The banks are able to extend the money supply to an excessive amount due to the presence of central banks and deposit insurance.

If the government allows the central bank to protect the banks in this way (and this is the major function of the central bank) than the currency of the state (the base money) will be threatened with dilution. By enabling the central bank to protect the commercial banks the state exposes its own currency to hyperinflation which would bring down the state itself in any meaningful sense. The state is vulnerable to collapse merely because it provides deposit insurance to the banks and doesn't constrain the activities of the central bank.

The central bank and deposit insurance have the capacity to destroy the government via hyperinflation because the commercial banks will issue unlimited credit if there are no constraints on them doing so.

Counterfeiting is theft from the state

In most jurisdictions counterfeiting of money is a crime. This is because the state is a legal entity which is different from other entities in that it is democratically elected and representative of the people. Since government-issued money is generally treated as valuable then it is possible to gain value by counterfeiting currency which detracts from the value of the rest of the currency and it is for this reason than counterfeiting of the national currency is a crime.

Counterfeiting is theft from the state.

Because counterfeiting is theft then when banks have deposit insurance they should be careful not to extend an excess of credit otherwise new currency must be issued to keep the banks solvent. If the banks are in the protection of the state they have an obligation to prevent the government from needing to bail them out. Bank insolvency (or even the risk of insolvency) is theft from the state if the bank benefits from deposit insurance. If banks have deposit insurance then they must stay solvent at all times (avoiding even the risk of insolvency) otherwise they are stealing from the state.

Counterfeiting is theft (from the state) and if banks have deposit insurance they must not allow themselves to become insolvent otherwise they are committing a crime (from the state). Banks steal from the state if they are insolvent and have deposit insurance.

Deposit insurance is (a form of) credit insurance

If a bank can't fail then the reason for this is that it is guaranteed by the state. The name of this insurance is usually 'deposit insurance' which sounds more benign than credit insurance. The term 'credit insurance' gets closer to elucidating (clarifying) the nature of the problem with the banking system. If credit (of any organisation) is guaranteed then this leads to inflation of the money supply. The term deposit insurance tends to refer only to banks but the problem would be the same if the credit of any firm is insured... it is not because the agency is acting as a bank that there is a problem. A deposit is only one kind of credit which is specific to banks so the complaint (or contradiction) is the 'insurance' not that the credit is a deposit and has been issued by a bank.

Not all counterfeiting is illegal

The nature of fractional-reserve banking is that banks (and their customers) are able to inflate the money supply and increase nominal prices. There is a difference between broad money and narrow money and the difference is that broad money is issued by the (state-guaranteed) commercial banks unlike narrow money which comes from the central bank. Without the state guarantee the commercial banking sector would not be able to issue money because unfunded liabilities would have no value. It is because the government is standing behind the banks that their (excess) credit has value equal to that of normal money. So when a bank issues a loan (or a mortgage) new money is being created and the bank together with the customer is increasing the money supply. And because it is the customer who initiates this arrangement then it is they who are in fact causing inflation. This a legal form of counterfeiting and so then people who borrow money are counterfeiting the currency. So then is it not always illegal for citizens to counterfeit the currency they are able to do so when they get a loan from a (state-guaranteed) bank. Counterfeiting is not always illegal since it is legal to borrow money from insolvent (state-guaranteed) banks.