It doesn't matter what device relays the code I typed over or otherwise transmits the approval through untrusted networks to the server
> The sad reality is that phones (and some tablets) are the only relatively secure computing environments that we have
My bank('s authenticator hardware) begs to differ
That's not what I am saying. The authenticator is irrelavant to this attack. If your machine is compromised by malware, the malware could take over the browser session, regardless of how you log in.
Phones are better protected against persistent malware because every application is sandboxed (harder to escalate) and much more of the boot chain/OS is validated (harder to persist).