Banks can't get rid of reserves at the central bank in aggregate. They can only get rid of them to other banks. So there is no need for the central bank to pay them.

You can't hold reserves so the bank can charge you for borrowing money.

Since there are more reserves than required, and no alternative source of interest, the inter bank rate would be driven to zero.

How do you think central bank rates bind? It gives banks an alternative source of interest other than lending them to each other.