Here one of my famous drawings:
Imagine this is a microscopic picture of the surface of the transistor (upside) and heatsink (down). The surfaces are NOT flat on a microscopic level but actually very rough. And THAT is the main role of the grease. If you don't use the grease, the contact between transistor and heatsink will be very minimal. THUS you have a terrible conduction of the heat from the transistor into the heatsink. The grease fills up the gaps and is of a material that conducts the heat easily into the heatsink.
If you have a mica plate between the transistor and heatsink, it just adds a layer in between, so grease must be applied on both sides. Mica is a kind of STONE (!) even though it's transparent. It will break like a stone if you bend it too far. So, you can imagine it will have a rough surface too.
Now, if you have air bubbles or dirt elements in the grease you can also imagine it will hinder the transfer of heat into the heatsink.
Anyway, I hope this awful picture makes it clear
After 30 years it is a good idea the replace the mica and thermal grease on critical transistors like deflection transistors on vector monitors. The mica and grease dry out over time and loose their heat conduction.
I have experimented with it on my Amplifone board. The transistors felt a LOT cooler after I had redone the mica's and grease. If you can feel a temp difference with your fingers, it's a pretty big difference because they are not THAT sensitive that you can feel a difference of a couple of degrees.
I would love to have a heat-camera or even temperature probe to do a one-on-one compare "before" and "after".
