Our financial markets are built on the idea that the assets being traded (in each individual market) are effectively fungible. It's the underpinnings of the whole structure of finance.

Companies are allowed to issue non-fungible shares.

Eg it's common in some tech companies to give the founders super-voting stock that reverts to normal stock on sale.

Yes, but assets that are traded within a particular financial market is fungible.

When you buy a share from the open market, they are not going to guarantee a particular share with a particular serial number you specify, they will only provide a number of that particular class of share of the company.

Well, only fungible shares lend themselves to be traded on financial markets.

Most companies decide to make their shares fungible, because they want them to be readily tradable.

But there's no one forcing anyone here. Companies and investors could agree to shares with particular serial numbers.

It's just so much more convenient to have fungible shares, that this is where all the capital goes.