Actually the spinning core theory is just a theory too. Sure it's based on some indirect analysis of observations, but all theories are like that.
"The change in the waves' speed showed that the fast axis was in motion relative to the Earth, proving that the core is spinning faster than the Earth, they said."
Wow. Who would have thought that changing wave speeds proves it's rotating. What a big leap of faith. See how indirectly they measured it? Their conclusion depends on all sorts of assumptions being correct. Most likely they are, just as the assumptions leading to the radioactivity theory are probably correct too.
Then you took a further leap of faith to suggest that this motion was responsible for the Earth cooling slower than expected or perhaps heating up. That violates thermodynamics which is based on a huge volume of experimental data. It would be a perpetual motion machine generating heat from nothing but its own magnetic fields, electric currents and friction.
If someone had a theory that flying monkeys were on the moon, of course I wouldn't give them the time of day unless they also had experimental evidence to support it. Maybe not their own experiments, maybe a new analysis of existing results. But if someone took photos of them, I'd be equally critical. Of course photos can be faked.
I think if you look up the radioactive decay theory, you'll find it's very palatable. There's no wild assumptions there. In fact why do you even doubt it? We find decaying atoms on Earth all the time. We know that generates heat. What's the problem?
