Too many economists focus on solely equilibrium.
It would possible for the yields on checkable deposits to always be at a level where households and firms are willing to hold the existing quantity. It would be possible for the yields on checkable deposits to always be a level where the quantity of deposits that banks choose to issue exactly matches the quantity that households and firms want to hold.
The first is a Marshallian-type equilibrium. The quantity of deposits is determined by the banks, and the yield adjusts each "market day" so that the quantity demanded equals that given quantity. It is like the fisherman bringing in the catch, and then the price on the fish market adjusting until all fish are sold.
The second is a Walrasian-type equilibrium. The Walrasian auctioneer calls out an interest rate on deposit, and each household and firm reports back the quantity of deposits they want to hold. At the same time, each bank reports the amount of deposits it wants to issue. If the two don't match, the Walrasian auctioneer calls out a new deposit interest rate. The natural approach is to call out a higher deposit interest rate if there is a shortage and a lower deposit interest rate if there is a surplus. Once the to match, then the banks issue deposits and the households and firms take them and hold them. The deposit market is in equilibrium.
Nothing like this occurs for checkable deposits.
For the Marshallian fish market, the existing quantity of fish must be sold for money during the market day. The money price of fish adjusts enough so that the amount of fish purchased equals the amount of fish that exist.
Checkable deposits serve as money and so there is no need for those who currently hold them to sell them for money. They can instead simply spend them for assorted goods and services, including other assets. Most importantly, there is no need for those receiving the deposits to want to hold them. They can instead plan to spend them on goods and services, including other financial assets as well.
There is no Walrasian auctioneer. In typical markets, sellers quote prices in terms of money and offer output for sale. Buyers then decide how much they want to buy with money. If the sellers run out of output at the going price, there is a shortage. If buyers don't purchase the entire quantity offered for sale, there is a surplus. The sellers then revise their plans and choose a price and quantity combination.
Again, checkable deposits serve as money and so those who want to hold them do not need to use money to buy them. People sell their products (including resources like labor) for checks or electronic payments, which when deposited increase their deposit balances. They then refrain from spending it. Further, those who were spending the money by writing checks don't necessarily intend to reduce their holdings of checkable deposits. Instead, they might intend to rebuild those balances from their earnings of deposits as they sell their products, including services. Still further, banks issuing new checkable deposits don't need to sell them for money and then use the money to purchase earning assets. Because the checkable deposits are money, they can be directly used to purchase the earning assets.
The banks issuing deposits or those currently holding them who want to hold less do not need to first sell them for money, and so there is no need to offer buyers a higher yield to convince them to accept the deposits. Those wishing to hold more deposits do not need to go to a deposit store and buy them with money. They don't have to offer to accept a lower interest rate to entice someone to give up their deposits.
These considerations explain why deposit interest rates do not immediately change so that the quantity of deposits supplied and demanded match. And further, they show why it is that the "HPE" (hot potato effect) applies to deposits that serve as the media of exchange. Those with excess balances in their checkable deposits spend them. They do not need to offer a higher yield on them to get sellers to accept them. Sellers do not ask buyers what is the current interest rate on the buyers checkable deposit before accepting a check. Nor to they quickly check the yield that they are earning on their checking account before deciding to give up their wares. They accept the payment intending to spend their receipts on other goods and services, including other assets.
The reverse situation is true as well. Those short on money can and do simply refrain from spending the balances. They don't have to "buy" the checkable deposits for money, offering a higher price and lower yield. Those who sell less and so earn less income reduce their expenditures as well. No one shows up to the bank offering to "buy" deposits at a lower interest rate.
The notion that interest rates on deposits will always adjust so that the demand to hold deposits matches the existing quantity is false. The notion that interest rates on deposits will always adjust so that the quantity of deposits supplied will match the quantity of deposits demanded is false. The reason is that checkable deposits serve as the medium of exchange.