If there is an excess supply of checkable deposits, those with excess balances spend them. Those who receive those payments now have excess holdings of deposits, and they spend them. This is called the "hot potato effect."
There is certainly nothing in this process that requires that the expenditures of deposits be solely on nondurable consumer goods and services. The excess money balances might be spend on any number of real or financial assets.
When the prices of these assets rise, this tends to lower yields. They are held because of a flow of income or services, and the value of those services relative to the current price of the assets is smaller.
If the interest rates that banks pay on deposits is assumed to be fixed, then the lower interest rates on other assets reduces the opportunity cost of holding deposits. This will increase the amount of deposits people want to hold. Meanwhile, the interest margin that banks earn from issuing checkable deposits will fall, reducing the quantity of deposits that banks find it profitable to issue. The surplus of deposits disappears.
In the special case where checkable deposits and some kind of uniform "bonds" are the only two goods in existence, then it is possible to imagine that people will be unable to spend deposit balances. If holding money is the only alternative to holding bonds, and holding bonds is the only alternative to holding money, then money will only be spent by those who prefer to hold bonds rather than money.
However, in the real world, where there is a huge variety of real and financial assets, as well as nondurable consumer goods and services, there can be no presumption that those spending deposits want to hold smaller deposit balances or those selling other assets want to hold more money. A person selling a financial asset for deposits will often intend to use the deposits received to purchase some other asset.
Still, if the interest rate on deposits is given, and excess deposit balances are spent on a variety of financial and real assets, all of their yields will be driven down, making deposits relatively more attractive to hold and less attractive to issue. No doubt there would continue to be many purchases and sales of consumer goods and services and a variety of real and financial assets. There would be no presumption that those spending deposits want to hold smaller deposit balances or those selling for deposits want to hold larger balances. Still, there would be no excess supply of checkable deposits and no room for the "HPE."
The problem with this scenario is the assumption that the interest rate paid on checkable deposits remains fixed when the interest rates on earning assets are falling. Given the costs of providing intermediation services, a banking system facing reduced yields will lower the interest rates they pay on deposits. With interest rates on checkable deposits falling in proportion to other interest rates, there is no change in the opportunity cost of holding checkable deposits. With interest rates on checkable deposits falling with other interest rates, in particular, the banks' earning assets, there is no reduction in the interest margin earned by banks and so no reduction in the quantity they choose to issue.
Rather than a surplus of checkable deposits forcing banks to raise the interest rates they pay on checkable deposits enough so that firms and households are willing to hold the existing quantity, to the degree that excess money balances are spent on assets and drive down their yields, the indirect effect is to "compel" banks to instead decrease the yields they pay on checkable deposits.
Superficially, this process exacerbates a surplus of checkable deposits. The surplus leads to lower interest rates, which by impacting the earnings on bank asset portfolios results in lower interest rates on checkable deposits, a lower demand to hold deposits and so an even larger surplus. However, the reality is that because the interest rates banks pay on deposits depend on what they earn, it simply means that there is no tendency for lower interest rates to close off the surplus of checkable deposits.
If there is a surplus of money, then the excess money is spent on a variety of goods and services, including a variety of financial assets. Those receiving the money now have excess balances, and they spend them as well. While the yields on financial assets may be driven down, checkable deposits are themselve a financial asset, and their yields will be driven down as well, because the issuers will only be willing only pay lower interest rates the checkable deposits.
Consider a different scenario. The quantity of checkable deposits is equal to the demand to hold them. The demand for investment falls or the supply of saving rises. This results in a lower natural interest rate. Lower interest rates will reduce the quantity of saving supplied and increase the quantity of investment demanded. Saving and investment return to equality.
As interest rates throughout the economy fall, the opportunity cost of holding deposits at any given deposit interest rate falls, and so the quantity of deposits demanded rises. Meanwhile, the banks' interest margin decreases, and so the amount of money they want to issue falls. The increase in saving or decrease in investment appears to results in a shortage of money.
However, what that ignores is the incentive of banks to change the interest rates they pay on checkable deposits along with other interest rates. By simply reducing the interest rates paid on deposits along with the interest rates that they earn, the banks avoid any shortage of money.
However, from the point of view of the banks, a decrease in interest rates due to an excess supply of checkable deposits appears no different from a decrease in interest rates due to a change in the natural interest rate--more saving or less investment or both.
Now, if people were only willing to accept deposits in payment if they wanted to hold them, and insisted on a higher interest rate to hold a larger quantity, then this would not be a problem at all. A surplus of checkable deposits would directly result in higher interest rates on deposits, while a decrease in other interest rates in the economy would directly result in lower interest rates on checkable deposits.
However, since those wanting to hold deposits do not have to go to a money shop and buy them, and those wishing to sell deposits don't have to find a willing buyer, there is no reason for deposit interest to adjust anything like they would if there were a Walrasian auctioneer adjusting them. Instead, the "hot potato effect" applies to money in the form of checkable deposits.