See all the pretty picture on the not a blackboard?? Good, don't even look at the last one yet as it is for the next class, the 'older kids' if you will.
You alluded to me being a child so I'll take this opportunity to teach a child who is not all that fast on picking up the big picture. You support of the theory that the liquid in question gets thicker as you go deeper and stops from becoming a complete solid as it would never move after that.
My reference to a child is because they know nothing so presenting something 'new' if it is in pictures and words the lesson will be over sooner rather than later. Your ego and extra sensitivity does not make the lesson easier, there is the dig that has to be there.
The quick way to dispute that is to say the distance between the atmosphere and the outside of the core has several layers that do not exchange material. There are a few density graphs around so it depends which ones you use. The ones I am using are useful as is even if the numbers and distances might be off some. What all of them show is a gradual transition is gone and a jump takes place, just like when oil and water occupy the same area, they sort according to density as do all liquids. Oil and water can transfer heat without any mixing and in a large enough volume the flow is smooth and both liquids are thinner the hotter they get, the hotter they get at a certain pressure the closer they are to the boiling point.
The less pressure and the same temp as a liquid the closer they are to the boiling point. Staying with that pattern is suggesting pressure can turn a liquid into a solid again. The red lava is about 800deg and it is brittle rock at 600deg. At 1200deg it is yellow and a thin liquid. When cooled it is 2.2. on the density scale, 5km down it is hotter and also thinner than the lave at 1200deg that is coming out in fissures that reach 200 ft high. It Hawaii it has also flowed along the bottom of the crust (2.9 density) and the magma that rises under the ring of fire rifts is at 4.4 density when it begins to flow away from the rift. It loses heat all the way along that to be at the 1200deg at the base of the volcano. Between the bottom of the crust (2.9) and the top of the mantle (4.4) is the the molten material that is between those two numbers.
50km is 900C (1600F) Bottom of the crust and top of the mantle, slight difference in density but viscosity is similar.
2,700km is 3,700C = about 1C rise per 1km depth increase Density goes from 4.4- 5.7 so that is about 1 per 1,000km The more detailed graphs have several layer in that 2700km so that mean material transfers stop and only the heat is transferred.
You also cannot have a hot-spot like Hawaii happen as that would be a rising plume in an are that is the middle where all the outflows from the ring of fire meet.
The next part, if there is one, brings in the boiling point of the rocks and that is where the pressure chart comes into play.