The tradeoff they made here has essentially zero impact on the number of times you need to verify their code, it's just a matter of whether you'd have to verify browser native authentication code or authentication code delivered through a website written in JS, at the moment you authenticate.
A concern like the one raised in this thread is certainly valid for websites that have expiring sessions, where you can switch accounts and log in and out of. And we certainly do need better tools around signature verification and version pinning for websites like we do for binaries (content-addressed networks like IPFS may have good answers there).
But for this use case, it's not a practical concern by any measure, and all this alarmism seems really misdirected.