This was kind of also addressed here:
Where does interest come from?
In that thread I quoted from G. Edward Griffin’s book The Creature From Jekyll Island (pp. 191-192) where he describes the same kind of scenario. But if you go through that thread that may help clarify some things as well. One thing to keep in mind is they don’t have to spend 100% of their interest payments back out every payment period…debtors could get paid from the holdings of other people in the economy who do not have to make interest payments of their own. Yes, eventually if the central bank never spent any money, it would come to reduce the money supply and at some point hold all the money in the economy…but that doesn’t even work in theory, as the bank would have to constantly be spending money just to remain functioning. Bank employees, janitorial services, electricity, paper, ink, groundskeeping, building maintenence…the myriad of things necessary to keep a central bank running mean constant costs, and constant outflows of payments of the money. And the bigger the bank gets, the more of these costs there will be.
But even still, this “one entity controlling money supply” is part of the reason people like Ron Paul argue in favor of competing currencies, so that you never have to worry about any real influence…because unless there are laws forcing everyone to transact in the one currency (legal tender laws), if one entity or group acquires enough to manipulate the market, people will just use something else.
(But in reality, it won’t ever even get close to that point because people will constantly be using something else…and as more of the supply gets concentrated with one group some other kind of money will more and more gradually come into use…meaning there would be no point to try and gain all the money in the system, because by the time you did it, the economy would be already functioning without it…meaning it wouldn’t be worth anything near as much as you paid to acquire it.)