Banks get rewarded (collect that difference between savings and lending) for properly allocating funds. A customer always has a choice to go to another bank that is giving a higher savings rate or lower interest rate on a loan. Competition will result in better rates and better allocation of capital. If they were to be "forced" to invest most of their earnings in infrastructure or anything else for that matter (i.e. they don't have the choice to do what they want with their money) I assure you that you would have worse allocation of funds, higher rates of default and a worse off banking system. This statement just seems baseless.
Since banks are such important entities, I feel like we cannot leave it in the hands of corperations,
What are corporations besides a group of people who are on their own accord decide to invest or work for one entity.