You can actually arrange a simpler experiment for this. Suppose that Lenz's law were reversed and induced currents reinforced the change of the magnetic flux. Now take a single loop of wire, and suppose that we produce a small current in it (with a battery or a magnet - it doesn't matter). An increasing magnetic flux is then created through the loop.
This changing flux will now induce a current in the wire loop. You'll see by the right hand rule and the modified Lenz's law that the induced current goes in the same direction as the existing current. So the induced current reinforces the existing current - the total current increases and so does the magnetic flux, which induces a further increase in the current etc... With a simple loop of wire you could power a city.
In the actual case the induced current resists the increase in mangetic flux and opposes the current already present in the wire, slowing and eventually stopping the growth in the current. This is the operating principle of an inductor.
The middle magnet is spinning, so it attracts and repulses the other two magnets once per rotation.
It is spinning "super fast" - that is so fast that the attraction and repulsion phases are super short. The other magnets are just too heavy to even start moving visibly in one or the other direction, before the direction of the force changes again.
We could say "nothing happens" - except the outer magnets oscilate slightly with each rotation.
If the middle magnet would spin "super slow", the others would just jump to the middle one, stick to it, and rotate with it as if it's all one magnet.
What happens if the middle magnet would spin with a frequency in betwen?
That's difficult, because much depends on how the rotation starts, and we only know it has started...
If the rotation starts slowly and gets faster then, up the middle speed, different things can happen during the first rotation. The magnets could stick to the rotating one, or move away a little bit; That whould have a big influence on what happens later.
Best Answer
They do attract one another. Indeed one of the biggest engineering problems in the building of very large scale electrical power generation hardware is the construction of generator rotors and stators to withstand the enormous stresses put on them by the magnetostatic attraction / repulsion between neighboring currents. The yoke of any magnetic system is in a state of constant internal stress owing to self force between its parts.