[jacquesm]

> Unless the spokes go slack, the tension does not affect the stiffness of the wheel.

Sure, but when they go slack you've lost the plot somewhere along the line. That should - in principle - never happen.

> Properly functioning wheels operate in the linear elastic region.

Yes, more simply put: they are non-deforming springs.

> Higher tension is related to higher ultimate load capacity and better fatigue resistance.

Up to a point!