Managers DO cross team boundaries though, their peers are other managers. I can't talk to the 100 people in my department every week, but my manager can talk to their 9 peers, who each talk to their 10 reports.

Precisely! And this is true not just for managers but also higher-level ICs. Its ok for Senior and below to be team focused, but moving to the next level means broadening scope and that means talking with people, regularly!, outside your immediate team.

And at larger companies, teams and groups are often geographically distributed if only in other buildings and office locations.

But the initial claim was that 1:1 meetings "add value to the team". I can believe that they add value to the manager's manager, but they are not adding value to the team of the person being met with.