I apply grease to the steerer tube because it passes thru metal/plastic spacers and the metal stem. These are metal-metal contacts, and grease 1) protects 2) lubes and 3) decreases squeeking noises.
The part of the steerer tube inside the headtube doesn't need any lube on it, however, as it doesn't contact anything. But a thin layer certainly won't hurt anything and may protect the metal as noted above.
The part of the steerer tube inside the headtube doesn't need any lube on it, however, as it doesn't contact anything. But a thin layer certainly won't hurt anything and may protect the metal as noted above.