Not very clear from the link summary, but I don’t think the inner core “reverses its spin” what is probably meant is that the mid-depth liquid realm and the metal inner core have always been spinning at slightly different rates and sometimes the inner core is ahead of the liquid realm, at other times (I presume this era since 2009) it spins a bit slower. But they are probably both spinning at similar rates. Whether they both spin at similar rates to the outer crust (where we live) or not, I don’t know. I’ll try to find out more details about all that. It would not seem very stable for the earth if they were not all three layers spinning at similar rates. Perhaps the differentials are quite small as in meters per day.
As to the theory that the outer crust might at various times suddenly stop spinning, that seems very unlikely to me. The earth’s rate of spin is gradually slowing down. The day if measured in modern time units would have been 21 hours long in the dinosaur era. The earth has slowed its rotation very slightly during human history. This was proved by comparing Sumerian eclipse records to what astronomers had calculated should have occurred at constant spin rates. I think the conclusion was that the earth had rotated through about one tenth of a day more than expected going back to 3500 BC so that solar eclipse paths were falling on regions further west than the calculations. If the differential was one tenth of a day, then the eclipse the astronomers had calculated should have been around Tibet or maybe southern China would have been in Sumeria (ancient Iraq) instead.
(That would assume their calculations of the new moon dates were correct, a similar outcome would occur if let’s say the moon was perfectly aligned with the Sun a tenth of a day later than expected)
These changes are not linear and I’ve read that the earth day shortened slightly in recent years (rather than continuing the longer trend of lengthening out). Maybe that has something to do with the other changes going on inside the crust in the liquid outer core and the solid inner core.
I could imagine faster changes in the length of day from some astronomical event on the order of perhaps many seconds or a few minutes per day but a sudden stop in the earth’s rotation seems to require forces that would be so powerful that in all probability the earth would disintegrate entirely.
So, what I discovered in the literature about the rotation of the inner and outer core is this — they are believed to be rotating faster than the mantle by 0.3 to 0.5 degrees of longitude per year. That means that over about 900 years (360/0.4 = 900) the inner and outer core make one more rotation than the mantle. The research being discussed in the linked article says that those two components are not quite rotating in sync, but does not specify the variations, you would have to imagine they are fairly small in relative terms, and the implication is that they average out the same.
In other words, these are fairly small variations, it’s not as though the mantle is rushing quickly over top of the outer edges of the liquid outer core. A difference in rotation of 0.4 deg per year is the equivalent of 30 miles at the equator and perhaps 20 miles in most parts of the United States. So whatever part of the core is beneath your home today was perhaps twenty miles west of there a year ago (since it rotates faster). That is a lot faster than the movement of “hot spots” in the crust like the one that has been moving through southern Idaho and under Yellowstone National Park in geological times. That hot spot is moving at about 0.01% the speed of the core in relative terms. I don’t have any idea if the two things are related in any way.
Correcting one statement in my previous post, the Yellowstone hot spot is moving a lot slower than I said, the rate of its eastward drift is about 0.0002% of the earth’s core relative to the mantle. The hot spot was north of Great Salt Lake about ten million years ago. It would only take the core about twenty years to move that far (relative to Yellowstone Park).