Ok, I see the confusion.
The Currie Effect doesn't apply to magnetic fields created by motion charge. It's only applicable to stationary magnets.
The core creates a magnetic field because electric charge is flowing around in the molten core, but a blob of stationary molten core would not produce a magnetic field.
In short, yes, people have thought this through.
Lol. No, it doesn't matter if a magnet is moving or not, heat will destroy the coherence of a magnetic field and it becomes paramagnetic. Motion doesn't factor into this. Irons Curie temperature is 770C.
You can't maintain magnetic properties under high temperatures. The claim of having any idea what's beyond 10 miles below the surface is about a verifiable as superman or going to mars.
It's not a magnet that's moving. It's electric charge that's moving, which is how magnetic fields are generated.
It's fine to say we don't know for sure what's down there. It is based on inference from indirect sources, but the model of what's down there is fairly detailed and does account for the major phenomena we do observe directly.
The iron wouldn't maintain a magnetic charge at those temperatures.
You've got it the wrong way around; electric fields are created by moving magnetic fields.
I don't know where you're getting any of this, but moving electrical charge (aka current) does create a magnetic field. Consult literally any textbook on electricity and magnetism.
Here's one source amongst many: https://www.studypug.com/physics-help/electric-currents-produce-magnetic-fields
