Do banks make profits by selling bonds to the central bank? I am a bit puzzled by the quote below, from here (emphasis mine):


  Modern monetary theorists have helped clarify the obvious point that private banks are not essential to the design of the system. It would be possible for the Federal Reserve to bypass the banks which profit by selling bonds to the Fed and, instead, invest the proceeds, for instance, in a public “Infrastructure Bank” [...]


So, central banks pursue open market operations by selling/buying bonds from banks or other financial institutions involved in these operations. Maybe the author is referring to the "buying side" of these operations, whereby the central banks buy short-term debt from banks?

Does this mean that banks only sell these bonds if they expect a profit? Does that also mean that banks only buy these bonds at a profit? How does this profit materialise? Through a discount/premium over the price at which these bonds are bought/sold? Or is the author simply referring to the fact that these bonds have positive nominal interest rates? (but these bonds are usually from the government, so it is not the central bank who is paying the interest)

Does this mean that banks are in every single transaction profiting from such operations?

(sorry, a lot of questions but they are very much related).
No, banks don't directly profit from selling bonds to the central bank. These bonds are sold at face value, there is no discount or premium, this is not part of the system.

My best guess of what the author means is that by selling bonds to the central bank, commercial banks get cash, which they loan out and make a profit on the loans. So commercial banks profit from selling bonds to the central bank in an indirect way. Attributing banks' profits from lending to the central bank is a bit of stretch though and not a very appropriate statement in my view, so I fear I might have misunderstood the author.

What the article seems to promote is already a reality in communist China, where state-owned banks lend at favourable rates. There can be significant problems with this approach of cutting out private banks, as the Chinese bad loan problem shows (although private banks can also accumulate bad loans, but maybe less so due to competition), but this is a different discussion.