That's a really interesting approach. Do you think that was too extreme? Like you could've at least done some documentation work in that time perhaps, or that it went well enough that you'd approach it that way again in the future?
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.
It's not 'polite' to bring up the 2nd, but it _is_ there. Imagine me/you/him/her doing something wrong and bringing down Prod for X hours. Then imagine your manager telling the director "oh, and btw he submitted his resignation 2 weeks ago, and in confidence he told me he goes to our ABC competitor". That-Looks-BAD, even if it was the most honest of mistakes and even someone else's fault. Once you 'stop playing', don't touch that jenga tower!!