The banks cannot lose because of the subsidy of deposit insurance

No one is too big to fail. If banks lend more than they have in excess, to spare, they will become insolvent and reliant upon deposit insurance, as it is impossible for them to fail with deposit insurance. Bank deposits increase the money supply, if they did not then it would be possible for the banks to fail. This enables the banks (and some of their more fortunate customers, if they have good timing) to extract wealth from everyone else. The banks can increase the money supply with new deposits, by selling this debt to customers, the profit to the banks is the interest paid, insolvency is not a concern for them.

The investment behaviour of banks is not a major factor in their profitability, all of them are insolvent, it doesn't mater what the banks do, they win because of deposit insurance, they cannot lose.