The ineffectiveness of "security training" is precisely why TOTP is on its way out - you couldn't even train Google employees to avoid getting compromised.
IMO most of this is because most security training I've seen is abysmal. It's usually a "check the box" exercise for some sort of compliance acronym. And, because whatever compliance frameworks usually mandate hitting lots of different areas, it basically becomes too much information that people don't really process.
That's why I really like the "Hang up, look up, call back" mantra: it's so simple. It shouldn't be a part of "security training". If corporations care about security, it should be a mantra that corporate leaders begin all company-wide meetings with. It's basically teaching people to be suspicious of any inbound requests, because in this day and age those are difficult to authenticate.
In other words, skip all the rest of "security training". Only focus on "hang up, look up, call back". Essentially all the rest of security training (things like keeping machines up to date, etc.) should be handled by automated policies anyway. And while I agree TOTP is and should be on its way out, the "hang up, look up, call back" mantra is important for requests beyond just things like securing credentials.
It's not just because it's abysmal, it's because it was found, empirically, not to work, no matter how good you make it. The mitigation you're describing is also susceptible to lapses and social engineering, just like what got them into trouble in the first place.
The simpler mitigation of 'the target employee with with the Google account full of auth secrets should have had it U2F protected' would have worked even if the phone person had just read out the target's Google password to anyone who called and asked for it.
They could have enforced that with a checkbox in their GSuite admin console.