> I suppose if their email is already compromised, that could be a problem, but this would require both the Key directory and the email account to be compromised.

How does the key directory get the keys, and how does it ensure that the keys are valid? Traditionally, key servers accepted any keys that were uploaded to them, and told people to verify them before trusting them. Some key servers will try to verify keys ... by emailing you. But, of course, if an attacker has compromised your email account, that doesn't help much.

With WKD, you contact the domain that owns your email account (e.g. if you are something at emailprovider.com, you would fetch the key from emailprovider.com). But if someone compromises emailprovider.com, then they could just serve the wrong key.

One of the goals of end-to-end encryption is that you don't want your service providers to be able to read your things. Both of the existing systems are vulnerable to attacks from your service provider (either if they become malicious, or have a rogue employee) unless you verify the key in some other way.