Immediately after WebUSB shipped in Chrome: "security researchers Markus Vervier and Michele Orrù detailed a method that exploits a new and obscure feature of Google's Chrome browser to potentially bypass the account protections of any victim using the Yubikey Neo".
The fact that fishing (and fingerprinting etc.) isn't reported widely doesn't mean it doesn't happen. After all you trust Chrome to properly implement everything and take care of things. And yet here's an example of a different hardware standard, WebMIDI: https://twitter.com/denschub/status/1582730985778556931 (note the comment: "Chrome still allows web developers to enumerate attached MIDI devices without user consent or even a notification")
In my opinion, the Chrome team overreacted and blocked all WebUSB access to any U2F/HID device.
Now if you want to update the firmware or configure your key you need to download an .exe and run it instead, which seems unfortunate to me.
If the phisher had said "Your U2F firmware is out of date, please download and run this update to continue", would that have been a vulnerability? That could also bypass 2FA (or anything else, for that matter).
I personally think it's no more plausible than "Your USB firmware is outdated, please run this updated to continue logging in". Malicious sites do regularly pretend to require software updates and ask you to install them. That can still and does bypass U2F today, and actually happens in the wild.
Sure, it's not a magic a wand that solves all problems, or makes malware disappear. I wish it did, but the fact that it doesn't is not a good reason to reject it.
It's deployed to billions of people globally, can you show me any evidence at all that there is any Web USB social engineering happening?