Keep in mind I'm not a tech diver, and am in the same experience bracket as you.... But from my research tech diving generally involves situations where immediate access to the surface isn't an option (due to deco obligations or physical overheads, or both). As such, they dive redundant air sources with the ability to isolate malfunctions (like doubles with an isolator manifold). They also gas plan with reserves according to the situation. A stage bottle is additional gas that is part of the plan (and may be a mix for specific portions of the dive).
For recreational NDL diving, I have a 19cf pony. It is effectively a buddy that never abandons me! I sling it on the front of my harness, and if I had to use it it's no different than OOA with a buddy (keep calm, establish an air supply, controlled termination of the dive). In an OOA situation, and you were on nitrox, would you refuse the alternate from someone on plain air?
On a side note, I suspect that the term "stage bottle" may originate from staging them in a physical location ahead of time. But I'm probably wrong!