Tracking stock ownership (at least in the US) is both messy and slow. And companies do either make mistake or do not honor their engagements (a la FTX, for example, by not actually having the stock and trying to procure it later when needed).
A blockchain solution can make settlements faster, final and prevent the current issues. It also means you no longer need a broker to hold your stocks/assets. More sophisticated users can run their own "wallet".