One function performed by private banks is to intermediate between borrowers and lenders, though they also create a certain amount of new money every year.
If there were no banks, then there'd be a big reduction in intermediation, i.e. while individual lenders would lend to individual borrowers, there'd be a big reduction in the total amount of lending and borrowing: that is, there'd be a big reduction in the total amount of debt. Put that the other way round: banks result in more debt.
Given that the word debt has negative overtones, that might seem like an undesirable outcome. Unfortunately, while overtones fool most of the people most of the time, they don't prove very much.
A classic example is the phrase "national debt", which the large majority of people and possibly even the majority of so-called "professional" economists believe to be undesirable. That's because (to repeat) the word debt has negative overtones, so the national debt must be bad, bad, bad. Incidentally, the overtones are even worse in the German language, which helps explain Germany's obsession with maintaining an external surplus, i.e. being a creditor rather than a debtor.
In fact, national debt can perfectly well be viewed as a form of saving, and if you like, called "National Savings". That is (as MMTers keep pointing out), national debt is very much like a deposit account at a bank, with government playing the part of the bank.
Anyway, is there a problem with the increased amount of debt brought about by private banks? Well, as long as debtors are able to pay the interest on their debt, there shouldn't be a problem.
In other words, to the extent that there are an excessive number of cases where debtors cannot pay the interest, i.e. where the lending is irresponsible, then clearly what private banks do is wrong: i.e. the increased amount of debt they occasion is undesirable.
Now what's the basic cause of that sort of that irresponsibility (e.g. NINJA mortgages)?
Well, one important cause is the fact that governments stand behind private banks. For example, there is FDIC insurance for small banks in the U.S. As to large banks, Uncle Sam dishes out hundreds of billions of dollars at laughably low rates of interest to large banks in trouble, as happened in the recent crisis. And as to the U.K., state backing for private banks has been provided free of charge since WWII. That is, unlike the FDIC system where at least banks pay an insurance premium, U.K. banks have obtained state protection for free until very recently.
But all the latter forms of state protection throw up a problem, namely: if the insurer pays when you lend in an irresponsible manner, why not lend irresponsibly and keep the profits when all goes well while sending the bill to the insurer when it doesn't? It's a heads I win, tails you lose scenario.
Of course, we couldn't just abolish all forms of state support for banks and leave it at that. But we could make money lending entities (aka banks) fund themselves in much the same way as any normal corporation, that is with substantially more capital than they currently do. Obtaining a third of funds from equity is perfectly normal for non-bank corporations, and Google (NASDAQ:GOOG) (NASDAQ:GOOGL) is funded 90% by equity. Google, far as I know, is not a disastrous flop.
It is hard to prove what the optimum amount of debt is. Thus it's a big over-simplification to argue that just because private banks increase the total amount of debt that the effect of private banks is harmful. In contrast, what does the real harm is the backing for private banks offered by governments.