The main advantage of blockchain-based credentials over PKI is replacing a single (vulnerable) centralized authority with (more durable) decentralized network for verification. As we’ve recently seen, CA’s fail all the time due to disasters or war, natural disasters, or technical disasters (i.e. Equifax). Even Adobe has recently been hacked, a massive CA for chain of trust PDFs. Beyond physical durability, the cross-border nature of this network makes verification potentially more convenient across jurisdictional borders.
And beyond the convenience for people and those verifying their records, there are also several technical advantages over traditional PKI techniques: https://medium.com/learning-machine-blog/trusted-timestamps-bbeb3d29cc0