I disagree with your logic. As the corner-cut solution shows, there are only two sane answers. "20 minutes" where you have cuts across the plank or "any* amount of time whatsoever" where you allow any kind of cut.
There is no sufficiently logical way to get to any particular number other than 20; the shape of the plank does not allow you to cut across and make your cuts intersect like you might with a square board. There is no reason on this particular shape to prefer "15 minutes" over "14 minutes" or "25 minutes". It all gets lumped into "any amount of time whatsoever".
If "any amount of time whatsoever" was an acceptable answer it wouldn't make sense that a single cut takes 10 minutes, so we should discard that answer. This leaves only one candidate answer, 20 minutes.
*"any" would be limited by how long of a diagonal you can make but it would be hours
There is no sufficiently logical way to get to any particular number other than 20; the shape of the plank does not allow you to cut across and make your cuts intersect like you might with a square board. There is no reason on this particular shape to prefer "15 minutes" over "14 minutes" or "25 minutes". It all gets lumped into "any amount of time whatsoever".
If "any amount of time whatsoever" was an acceptable answer it wouldn't make sense that a single cut takes 10 minutes, so we should discard that answer. This leaves only one candidate answer, 20 minutes.
*"any" would be limited by how long of a diagonal you can make but it would be hours