A non trivial question about a current carrying loop in a changing magnetic field

We all know that a current carrying loop in a changing magnetic field will by Lenz's law experience an induced current to counteract the change of magnetic flux. But why doesn't anyone ever suggest that the plane of the loop could rotate to present a smaller or larger area to the magnetic field, perhaps in conjunction with a smaller induced current? Isn't the rotation of the plane of the loop also a valid solution to restore magnetic flux?