The issue is there is no incentive for the person leaving to make these handover docs and videos. They will just say the bare minimum and complete the task.

The incentive of leaving a good last impression on your employer, so you get a good recommendation, is a pretty good one, imo. It might actually be much more valuable than anything else you do in those last days/weeks, in fact.

It is true that your reputation follows you, but how are going to judge whether the knowledge gathered from that video is sufficiently thorough without actually watching it or at least going through generated notes. This will be generated and left for another llm to summarize and forgotten on a drive somewhere. No one will see any of it unless there is an actual issue.. at which point, it likely won't matter for the purpose of recommendation.

A handover happens not only when someone leaves the company but also when one moves internally. In that case the incentive to prepare the next person is definitely stronger.