You are 100% right that tension is a critical wheel dimension.
Interesting tool, although I`m not a wheel builder. Its a real craftsmanship ;)
I think the big difference between your use case and mine is simply that I don't have the luxury of rebuilding my wheels every three weeks but they have to last for years. I'm sure that if you treat them as disposables that you can get much closer to the limit, but the bike shop where I worked built ordinary bikes for ordinary people, and then long term reliability is far more important than to squeeze the last little bit of stiffness out of a wheel, though I can see that even in that case there might be some gain from being able to do that.
Keep in mind that this was - and in many places still is - a pretty low tech affair and broken spokes on a bike through normal use on a properly maintained bike in principle should not happen. Usually that indicates that either something got abused, badly mounted or left without maintenance for too long.
Higher tension is related to higher ultimate load capacity and better fatigue resistance.
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!