Banks should instead act as service providers in managing the bilateral creation of the necessary "trade" credit.

That's EXACTLY what they have done in recent years (in fact, it's the very definition of what investment banks do), and it's at the root of the problem: given that they have no skin in the game to speak of, they don't really care if the risks are bad, as long as they manage to dump them on naive or greedy investors.

Fools and greed will never go away. Thus, a working bank system has to structurally limit their ability to do stupid things on such a scale that it becomes a systemic problem. Having banks as irresponsible service providers is NOT the way to do that.

In the long run, we're all dead. John Maynard Keynes