Banks aren't coin dealers; they're experts in money, not numismatics.
Here in this country, all the banks are obliged to receive gold and silver coinage (either the old, obsolete stuff or the modern collector and bullion coins) and credit the depostier the face value of the items deposited. A shilling's face value is 10¢, even if there's $1 to $2 worth of silver in a shilling. Likewise, a gold sovereign is credited as $2, even though the bullion value is around $200.
What the banks do with the stuff once they receive it, is up to them. The bank itself can't sell them for a profit; they're supposed to return them to the Reserve Bank, who would then pass them on to the Mint for melting down and re-issue as new coinage. In practice, this is a tedious and bureaucratic process, and the banks prefer that the tellers dispose of them by other means - either the tellers themselves "buying" them for face value out of their own pockets, or "re-issuing" the coins (again at face value) to someone who asks for them.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis