I used thermal adhesive to connect an aluminium cooling block to an aluminium plate and discovered that "thermal" adhesive has about 500 times less thermal conductivity (0.9) compared to aluminium (600).
I'm not sure why thermal paste should be used at all as it is far less conductive than the metals themsleves.
The problem is the air (insulator) and tiny gaps between the CPU and the heatsink, the paste or sheet can fill those tiny gaps. Theoretically its possible to use no paste at all, but then the CPU really gets hotter by some degrees during load.