"I am still skeptical of this kind of energy argument. It strikes me as
a Kiplingesque just-so story. The problem is, if you teach students to
make this argument, they will apply it to other situations where it gets
the wrong answer. As an obvious and important example of what I'm
saying, suppose we set up two masses fairly near each other in
otherwise-empty space. I drag one mass toward the other at a steady
rate. So far, this is very closely analogous to the wire-on-rails
example. So far, so good. ☠ Now we make the argument that if there were
a force in the same ☠ direction as the imposed motion, it would allow me
to get energy ☠ "for free". The system would be unstable. This obviously
cannot ☠ happen, so ............"
But it sounds like you are disagreeing on pedagogy and not with the
physics. My first goal is to do no harm. In this case, it is not wrong
to claim that a current that were to flow in the direction opposite to
that required by Lenz's law would produce a result that violates
conservation of energy. I'm not saying that it is unstable. I'm saying
that it produces energy we can't account for.
Your example with two masses is a different case, not just in the
particulars. First, those masses will attract each other whether I drag
one or just let them fall together. So I don't see that as a stability
issue. In fact, to drag one at a steady rate, I'll have to pull it in
the opposite direction of the motion. But setting that aside, the key
difference is that as the blocks gain speed, there is no mystery about
where that energy comes from. The potential energy decreases. I can't
identify a similar decreasing potential energy in the u-circuit example
that would account for the energy that would appear should Lenz's Law be
violated.
Similarly, if I drop a magnet down an aluminum tube (commercially sold
as a Lenz's Law Apparatus), the induced currents flow to as to inhibit
the fall. As the magnet drops, much of the lost potential energy is
converted to heat as current flows in loops around the tube. If the
current were to flow in the direction that sped the fall of the magnet,
how would we account for the greater energy?