Of course spokes work through tension, I never suggested otherwise. But a spoke is also a tension spring, it is not rigid, it has a defined spring rate dependent on it's dimensions (why we and our spoke length calculators calculate final spoke length with some consideration of the spoke gage).

How could one conclude that the elasticity of the spokes would not affect the stiffness of the wheel?

When a wheel sustains load, it flexes, and the spokes flex (elongate elastically) when this occurs as well.
So it goes without saying that making the spokes less elastic will reduce the flexibility at the rim as the built wheel sustains a varying load.
It's the same reason why different numbers of spokes affect wheel stiffness, and is one reason why straight-pull spokes have allowed today's wheels to achieve their stiffness with fewer numbers of spokes.

The benefit of higher spoke tension is that the rim can be deflected further before any spokes reach a point of zero tension, and thus of those critical few spokes no longer responding to increasing rim load with any further change of their tension. Higher tension does almost nothing for wheel stiffness up to this point of loading, other than present a straighter load path where the spokes may be crossed.

It sounds as if you are assuming that a spoke sees no change in tension in response to loading applied to the built wheel's rim. But spokes do see changing tension and elongation from even very small loads applied at the rim, easily verified by plucking a spoke, then pushing sideways at the rim and plucking it again. This is how I sometimes achieve higher final tension in the truing stand, when nipples may otherwise begin to gall an eyelet-less rim, or when a used wheel has corrosion issues at the nipples.