I think it was mostly a matter of not wanting to put the pawn where the bishop could get at it. But that is lazy thinking. With the knight at b6, the formation is solid enough to draw. White finds the correct plan. The king will infiltrate via d5 after Black eventually runs out of moves.
Passive play is unpleasant.
Being ground down by a Grandmaster is often even more unpleasant, as reprieves are rarely granted. I figured that I couldn't keep the king out forever, so might as well get it over with. Otherwise there is no way to make progress. Kf8 57.Ke4 Black must give way. Kc4 69.Bc2 Black wins, because the bishop is of the correct color to support the a-pawn.