I think you're missing the point. There is no such KLM official rule about this, its not in the SOP.

I say this because I got in contact with one of the Cabin Service managers after this bizarre experience happened to me.

Based on your arguments, all airlines should have such a rule, but they don't and neither does KLM.

Whether or not airlines require certain behaviors for an actual emergency landing is another point of discussion. The OP was not involved in an emergency landing. I'm quite sure a pax would be the least concerned with reading during an emergency landing. Why is this even worth mentioning, its not a point of debate?

It's very difficult to read something during the take off role and actual landing due to the movement of the aircraft so I always store my reading materials for those parts of the flight. But being told (as I was) that reading it during taxi and after the "10 minutes to landing" is stupid. For example a taxi to/from the Polderbaan or at LHR can take an age.

Anyway, thankfully, there is no such rule and that's the end of it.