It's strange that banks are allowed to make loans

It's unusual that banks are allowed to make loans given the existence of deposit insurance.

There is no reason for the government to let banks make loans... it would be normal for lending to be prohibited given that deposit insurance exists. If there is deposit insurance we can expect (it is normal) for bank lending to be prohibited.

It's weird (inconsistent*) that the government would let banks make loans given they have deposit insurance. If banks have deposit insurance then when they extend credit this increases the money supply. There is no reason the government would want to give this privilege to the banks.

*If the government wants to increase the money supply it can print money (and spend it) itself.