Seat posts, especially of a different metal to the frame (e.g., carbon or alu seatpost in a steel frame), regularly seize in place without grease (from galling or corrosion). Often in a matter of months. I’m amazed you’ve never run into this or heard of the idea in 15 years of professional cycling. Did you ever work on your own bikes?
If you’re looking for more friction than grease, you can use carbon assembly paste. But either way, you want something between post and tube.
Source: Profession cyclist for the last 15 years.