Sure you can transfer ownership by going to a company, getting approval from the board to update the cap table, and then executing the transaction via wire transfer. Or you could do it near instantly on the blockchain.

And how would you write an option on your ownership stake using conventional technology? That seems like it would be prohibitively hard.

How would you use your ownership as collateral in a loan? The illiquid nature of private stock may turn some lenders off. On a blockchain, the collateral can be part of the smart contract.

Many technological advances simply make already possible things easier. For instance, checks were around since the time of the Crusades. Functionally, checks transfer money from one account to another. We also have a postal service we can use to send checks almost anywhere in the world. So why do we have digital banking infrastructure and wire transfers?