I've actually done that before.

Nonrev outbound (wife would have driven to the airport to pick my kid up if she didn't get on or I got re-assigned).

I bought her a ticket home on my return flight. If something happened to that flight I would have tried to get her on another airline solo. Conveniently, the OAL flights in question went to large towns where we happened to have family.

Fairly low risk, it was out and back with long layover and not much else they could assign me to after departing base. But I was prepared to call the company and tell them they either needed to get my kid on my flight or I would have to stay until I could get her out. Having bought a revenue ticket would have hopefully mitigated the pain of that conversation.

Kid in queston is mature for her age, and had previously done solo domestic nonrev from a young age (obviously with family/friends waiting to collect her at the destination).