This should be a face issue if this theory is even half correct
This custom varies from Country to Country
You Have been given a Cheque you take it to your bank and hand it in all signed....
You cannot cash it immediately because it has to be "cleared" (you can go to some shops in the UK and get cash less a commission charge almost right away after showing Good ID)
The clearance period is 3 days in the UK
and can be withdrawn on the 3rd day bar a "bounce"
But once it's in your A/C it's your money and gains nothing except adding a few pennies to your Interest total(annually about 2% )
Ok this is what happens In my theory the money in those 3 or so days whether real or not goes into the Banks cashflow Kitty and Is invested on the stock markets making Millions per day and a tidy profit for the Bank (couple of Million? )
Dont think there is any "Real" check bar to see if there is a "Stop" on the cheque? then the theoretical "Money" is not in play (see next)
Thats all Bank notes Really are "Promissary Notes" look that up on a search engine . from the notes inscription(Parody)They promise to pay you (see Bank of England history) the sum of.. It is a virtual credit note dating back to the Middle Ages
In reality the real money I saw somewhere(I think it was on Answerpoint (our old Home) as a reply?) was the accumulated funds of Several Families about a Million pounds pooled as startup funds for the Bank of England (and they got these credit notes when they wanted spending funds)
Yet I do know this They would be easily Billionaires if their decendants wanted their cash out plus interest
But they have all disappeared I'm sure many of their decendants are unaware they have a share of this fortune only a handful of people know( and it's all theirs!! )
And it's not me My ancestors are Irish

I'm not sure exactly what your question is.

Here in the US we too have to wait for a check to clear the bank. If you have the funds in your account to cover the check, those funds in your account are put on hold and the bank will give you the cash. If I have $100.00 check and $500.00 in the bank they will give me the 100.00 and put a hold on $100.00 in my account. My available balance until the check clears is 400.00. (Cashing the check is really the same thing as withdrawing the funds) If you don't have the funds then you need to deposit the check and wait for it to clear. This could take 1-7 days depending on where the check is issued from. As for the banks investing your money while you wait.. Of course they invest that money! That is their business. I personally think the real money is made by direct deposit. The funds are in your account the day before you are allowed access to it. This is where the banks are doing the real investing of your money.

Money managers in large corporations play the same game, although at today's rates the return is not nearly what it used to be. Sadly, many seem to have resorted to unilaterally extending their credit terms to satisfy this income stream.

I worked in a bank many years ago. At the time, our most severe losses were in overdrawn accounts. Careful management of demand deposit (checking) accounts is essenential to successfully operating a bank.

Practice in the States is to permit same banking day credit for most deposits into personal accounts. This decidedly favors the consumer.