WebAuthn goes to great lengths to preserve user privacy, much more so than past alternatives, so I don't think there's a expansion of information, especially when the device is probed for capabilities which is extremely pervasive with browsers today. There is some new info with attestation, but other than it not being very widespread in practice, attestation keys are shared by a minimum of 100k devices.
In general, the intent of attestation seems to be enterprise use cases where companies want to issue authenticators that meet certain capabilities, and only allow those capabilities as attested by a trusted party. For instance, a company might mandate Webauthn with user verification for their internal systems, and they don't want an employee using a software based virtual authenticator that fakes UV and keeps key material in plain text, so they issue Yubikeys to their staff and only allow Yubikeys to be used for logging in (issued or otherwise, as the RP can't differentiate them). I have not seen a single instance of attestation being used to gatekeep access to an otherwise public service, but I'd like to see some examples if there are any. Enterprise attestation is a different beast, however, and can uniquely identify an individual security key, but this has significant management overhead and will not be seen outside of enterprise use cases.
Now I understand you personally don't value attestation as highly as some other features of WebAuthn and that's fine, I'm on the same boat. However that's the nature of standards and how they come about, there's multiple interests in the working groups. It's hard to say what's the "biggest" security increase because that's entirely relative to the individual or corporation implementing, consuming, or standarizing the functionality.
As to whether there can be a phishing-resistant trust-establishment mechanism, I absolutely agree that there can be. All I'm saying is that there isn't an interoperable one currently, and that it's hard to establish interoperability across vendors and without an online sync fabric (I'd presume most users would want to export key material to a file or otherwise not rely necesarily on a third party phone-home service to export keys). I also think that it exceeds the scope of FIDO and will have to be primarily OS-vendor-driven. For me, personally, this along with something like the recovery extension that Yubico is promoting is one of the potential future features I'm most excited about.
Related, and for the other reason why import/export is hard, which is the reasoning about the ecosystem, I don't think that even with such a mechanism we'll ever be able to export keys out if iCloud Keychain and into KeePassXC. What will most likely happen is that credentials generated by KeePaasXC and backed by hardware, will be able to be imported/exported in/out of devices in the same trust circle, using a KeePassXC sync fabric as the sync mechanism.