The authorities and manufacturer also require that sufficient fuel be carried for the intended flight, and people don't do that, so why would they carry and refer to the required checklist? The Canadian wording is the the approved checklist "be available" to the pilot (like fuel, I suppose) how the pilot uses it could be a different thing, but don't get caught in trouble not using it!
If you are using a home made or flying school made checklist, and something has been omitted, or confusion introduced by non approved additions, you, the pilot using that checklist, become responsible, not the person who wrote it!
Yes, I was required to have and use a paper copy of the checklist for my C 150 when I flew it for my CPL ride. (I had more than 2500 hours in that plane at that point). I exactly copied the one from the POH, and all was good. For those three or four flights, I used the checklist. When I flew an MD500 yesterday, the other pilot and I used the checklist (as I don't fly those very often).