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This is what is known as 'observational bias': you select favorable situations, and ignore those where the performance of the King did not impress you so much. No doubt Lasker did the same.
But a fact is that a King loses more often than not against a single passed Pawn. (Let alone against N+P or B+P.) So K < P. Now take that in your average...
So you noticed that when a King is in a position to fight, it fights pretty well. Unfortunately it quite often is in a position where it isn't able to put up any sort of resistance, and you conveniently ignore that. But it does strongly suppress the value a King has in real life.
A Knight has better chances to stop B+P than a King.