In favor of Reddit managing the ledger centrally? That doesn't allow for the public transparency that they would like, and it would probably be much harder legally (they would be stuck doing a bunch of KYC/AML stuff, which doesn't really make sense for a company like Reddit to need to deal with).
By transparency, I mean for example Reddit manipulating the ledger if it was on a central database. They could take away someone's shares, or give someone extra shares, and the community would have no way of knowing. If they issued someone more shares on the blockchain, everyone could see it happening and prove it. Anonymity isn't a factor here.
The point I was making on KYC is that with blockchain-based shares the government doesn't even have an idea of how to regulate it yet, and Reddit can probably sidestep the KYC entirely. Anyway it's not them managing the books, it's the Bitcoin network doing it for them.
Blockchain transparency isn't a bug or a feature per se, but the fact that it's truly decentralized is a feature. For Chaumian ecash, anonymity is a feature, but it's centralized. Stellar (or colored bitcoins, if they ever get around to implementing that) actually provides an interesting combination of features.