We saw, in the simple model in which the grower profits, an increase in the proportion of the total money supply owned by the bank. Does this mean that over time the bank will end up owning all the money?

Hypothetically, this could happen.

Even for the bank, however, money serves only as a medium of indirect exchange. Accumulating more money does nothing to increase the bank's economic well being. Since the principle of marginal utility applies to the bank, as well as any other economic actor, at some point the bank will prefer to exchange additional units of money for other goods. Whether he exchanges money for consumer goods or investments, we cannot predict, but we can predict with certainty that eventually he will cease his accumulation of money. More money for the sake of more money, at some point, does the banker no good.

Also, we can apply the reductio ad absurdum test. If the bank approaches total control of the supply of money, the market will shift to another form of money, putting the bank out of business.