Let’s try this again.
When a shareholder requests certificates, the broker MUST provide them (usually for a fee), but it is not uncommon for the broker to not even have them in their inventory and they then need to actually acquire the stock at market price. The "easier and better" ways you are referring to are the practices of letting customers buy and sell shares electronically, but HOPING that those customers never actually try to claim ownership of those shares via stock certificates.
And if there is an inventory check, it would be no different than a certificate check. The TA and lawyers will want to know that a broker that credited 500K of shares to a client actually has those shares on their books. As I've stated before, the majority of brokers will NOT hold their own inventory of shares for OTC tickers, but they MUST credit you with the shares if you successfully buy them. They then need to ensure that they have those shares on their books. They are HOPING that clients sell the same amount of shares that they bought before they are ever asked to actually deliver…as that clears their books and relieves them of future scrutiny. If they are asked to deliver and don’t have the shares in their inventory, then they will need to obtain them...at whatever the current price is.