Could someone please explain the need for “liquidity” in the stock market for publicly traded companies? Asking for educational purposes.

The question goes for both the stock itself, and cash. The only things I have found online are blanket statements such as for the purpose of improving market efficiency and for settlement purposes. It is difficult to find any deeper explanation as to how that is a benefit though. My low level understanding of a simple transaction in the stock market itself is that an individual deposits money into a Brokerage account, individual uses their funds to place an order to buy a stock, the order goes to a Market Maker who matches the order with a sell order, the sell order had been placed by a second individual who receives digital payment from the first individual. Any fees are baked into the first individual’s cost of buying the stock. So if brokerages and market makers are not utilizing customer funds for anything else other than facilitating the transaction, why is cash liquidity needed? If a stock is actually sold when the stock is bought, why is stock liquidity needed?

I understand the need for liquidity in say our banking system, which is based on fractional reserves, makes sense. The stock market is not a fractional reserve/trading system, not legally at least. Things have come to mind such as brokerage accounts on margin; ok, but the brokerage account cannot utilize customer funds, so if they are allowing accounts on margin, they would need the underlying cash to backstop that margin loan, is that not why they charge fees for margin use? As for the stock itself, there seems to be this underlying sentiment that any stock should always be available for sale, even if it is not actually available. Where does this notion come from? In no other market or supply-and-demand situation have a seen such an illogical occurrence. If something is not available for sale, then it is simply not available. By making something available that is not truly available is equivalent to counterfeit.

I hope the explanation to my reasoning makes sense, tried to cover a lot without making the post too long. If someone has some sound reasoning as to the liquidity need please help educate me on this, I have found nothing of significant detail through my own searches.