The "Hot Potato Effect" applies to checkabe deposits.
Suppose the quantity of checkable deposits rises beyond the demand to hold them. Those holding excess balances in their checkabe deposits spend the excess funds. Those receiving the payments now have excess balances in their checkable deposits, and spend them as well.
What brings the process to an end? The added expenditure on goods and services results in higher prices. The higher prices reduce the real quantity of checkable deposits. Alternatively, the higher prices raise the nominal demand for checkable deposits.
One the price level has risen enough that the real quantity of deposits fall to the real demand, the HPE is at an end. With the alternative framing, once the price level rises enough so that the nominal demand for checkable deposits rises enough to match the nominal quantity of deposits, the HPE ends.
Suppose that banks pay competitive interest rates on checkable deposits. Does that mean that the HPE no longer applies? Not at all. Interest on checkable deposits increases the real demand for checkable deposits. Given the price level, this is an increase in the nominal demand for checkable deposits as well. Still, if the quantity of checkable deposits is greater than the demand, then those with the excess balances spend them. Those receiving the funds now have excess balances. When the price level rises enough so that he real quantity of deposits falls enough to meet the real demand for checkable deposits, the HPE ends. Alternatively, the price level rises enough for the nominal demand for checkable deposits rises enough to match the nominal quantity.
It would be possible, of course, for the banks to increase the interest rate paid on checkable deposits enough so that the nominal quantity demanded equals the quantity. But why would the do that?
When someone goes to a shop to make a purchase, the seller does not insist that the deposit the buyer uses to make the payment pay a sufficient interest rate so that the seller will be willing to hold the deposit. The seller cares nothing at all about the interest paid on the buyer's deposit, because he intends to deposit the check (or electronic payment) in his own checkable deposit.
Obviously, it would be foolish for a seller for some product to negotiate with the buyer regarding the interest rate paid on deposits by his own bank. What does the buyer have to do with that?
However, the key element to understanding monetary theory is that the seller of some product or asset does not make a sale only if he is willing to hold a larger balance in his checkabe deposit. Sellers accept payments all the time intending to then spend the money on other goods, services, or assets.