I struggle to justify it from a cost and utilisation perspective. Given how well it went, I've run the hypotheticals in my head a few times about what the optimal case might have been. If you discount the cost of my time to zero and you assume the company could mandate whatever period is optimum for them I think the duration ends up being around 2 months. Mostly because we had a monthly billing/invoicing cycle we were part of. So one month as the forcing function to catch and document all the process, and then a 2nd cycle just to make sure you can apply everything you learnt.

My time wasn't at a zero cost though. But... at a high level, given the size of the company I worked for + the potential impact of getting something wrong, ~6 weeks of my time is pretty close to zero from their perspective. It also probably helps that we had pretty low employe churn.

But from my perspective it did feel like a bit much. Within a couple of weeks I was pretty bored. I was itching to help and do things like you suggested such as documentation, but the team saw doing the work of writing the missing documentation being part of the work of learning what the gaps were so I had to stay away. Ultimately I spent most of my time planning the next phase of my life and hacking on side projects, or hanging out in the common areas with my wife and newborn son when they'd come in.