Yes, and that's great if everyone agrees to trust the CA. Now try to solve the problem if they don't. I guarantee that your solution will look a lot like a blockchain.
I think that’s an important point because it touches on the challenges of a blockchain: if trust can be based entirely on the information in the chain, it can work. If security depends on outside oracles, legal enforcement, or other trust relationships anyway, you don’t need the expense of a blockchain relative to something like a distributed signature system. This is why the supply chain stuff never goes anywhere unless it pivots because the hardest part is trusting your auditors, and the expense / fragility of an always-on networked system isn’t worth it when it can’t solve that problem.
You don't need blockchain for this. I've worked in this space (the non blockchain part of online trust), tamper proof logs is already a service provided by central Certificate Authorities. All you need to do is to continuously sign a log and the CA can keep the chain of signatures, and thus provide proof that you didn't tamper with the log. That way the CA can both validate the identity of the signer and validate that the signer didn't tamper, meaning it is a better service than blockchains.
https://en.wikipedia.org/wiki/Anti-tamper_software
There is great value in software signatures. But that value is already captured and used everywhere, in SSL, software signing, document signing etc, blockchains doesn't add any value at all to that space as far as I've seen.
> Using a signing authority requires everyone to trust a third party. That can be difficult.
Finding a third party both trust more than they trust each other is trivial in almost every transaction. When you buy from Amazon you trust your bank more than you trust Amazon, and Amazon trusts your bank more than they trust you. Your bank is the third party. Can you name any significant usecases where there isn't a third party both participants would trust more than they trust each other?