Any idea which carbon? Carbon 'paste' is essentially a grease with a friction additive, so I'm struggling to see where the issue is...
There is an issue. Grease easily emulsifies where there is water and movement.
The presence of water is obvious, but movement not so obvious. The frame/seat tube joint and, the quill stem/steerer tube are two joints known as dynamic joints. In other words, they are not perfectly fixed but there is always movement. This is because a tube is inserted into another tube and only clamped at one end. The loose end is free to move as you apply force to the tube.
Now, if there is grease in there and water, the water is massaged by the movement to form an emulsion with the grease.
Emulsions are dangerous things in situations like these because the water cannot evaporate but is still available to do bad stuff, such as corrode or assist with galvanic action to corrode. Both aluminium on steel, aluminium on aluminium and, aluminium on carbon, is very prone to galvanic corrosion.
It is my experience that carbon assembly paste does not emulsify and therefore poses less of a problem with frozen seatposts and quill stems.
The invention of the Aheadset solved the quill stem issue but we are still stuck (no pun intended, as they say) with the same stupid seatpost clamp as 100 years ago, which is prone to getting stuck.
Carbon paste, in my experience, presents less of a problem.