If you've tried to battery start a Lycoming, and run the battery down with no success, a hand swing of the prop will no longer work to start it, you're going to have to use ground power - so, having the POH, to assure the proper connection and operation is a good idea!
where do you stop? Tool set? Lifejackets? Spare spark plugs?
But on the other hand, where do you start? Checklists are required by regulation, a POH by regulation, or often the type certificate data sheet. It is not optional for the pilot to carry something required (which could include lifejackets - I wear mine). If the regulations were to be relaxed, so that the booklet which seems to have been lost, and does not fit well in the cockpit is not required in a small plane, at what point does it begin to be required?
We'd agree that a large plane should have one, so the crew can refer to manage the systems well, where would the don't need it/do need it line be?
I remember ferrying a Lake Amphibian for a friend. I had enough time flying Lakes, but this particular one was new to me. It was to be a longer flight, so I filled up the main tank, and the two wing tanks. There I am, a few hours into a very nice flight, and decide that it would be wise to use some of the wing fuel, so my main tank was still useful for approach and landing later. I could not figure out what I had to do to access the fuel I knew that I had put in those tanks - I could not find any valve or pump to operate, I read ever placard I could find - nothing. So, I found the POH, and read it, everything relevant to the fuel system - nothing. But I wasn't expecting to find a reference anyway, I knew that these tanks were an STC.
So, I used the "phone a friend" option. I did not want to phone the owner, as I would look pretty silly, so I phoned another friend. I had to wait until I had crossed a large lake to get cell coverage again, and now I was in the US, so I was paying roaming charges. After all of that, it turns out that the wing tanks just drain into the main tank, when it gets down a bit, no pilot action required - and nothing written anywhere to explain it!
Having the POH and checklist may only be a part of what you need, there might be important supplements too...