The only real advantage that I can see is if the tokenised shares can be traded on a decentralised platform, which could open up a global marketplace of trading shares without having to physically open an account overseas. That would be tremendously useful for global security traders, in my opinion. But even then, it would lead to a lot of compliance and regulatory considerations which means that it's probably going to be considered by a select few companies with special circumstances.
that's the ultimate value of tokenization---the ability to trade on secondary markets (including p2p, DEX) without directly dealing with the broker/issuer. one could avoid KYC or jurisdictional limitations, or even invest without access to formal banking.
the problem, as we're beginning to see with stablecoins like PAX, is that this can put the fungibility of tokens in jeopardy. token issuers can't stop people from freely using tokens like any other cryptocurrency, but they can hassle you when you try to
redeem tokens and they can freeze your funds once you've deposited them for redemption. this will ostensibly be done for AML purposes. i'm curious to see how this all pans out over the next decade or so. it's a legal clusterfuck.