My electric company gave me a number (UID, not phone number) to resume a call if the issue wasn't fixed within 24 hours, and I'm pretty sure internet operators have the same protocol (at least used to).
Can literally be a "Desk ID" basically, so using that would reach the phone next to the agent. Used to work both with outgoing cold calls and incoming customer support, had a setup that worked like that for the latter.
> My electric company gave me a number (UID, not phone number) to resume a call if the issue wasn't fixed within 24 hours
What planet do you live on ?
Seriously. Where I am it is guaranteed that a utility company would never even consider such a concept let alone have the technical competence to actually implement it.