Can you generate your own HDRI maps without using photos? For example, preparing a scene in Maya using standard lights and rendering out a panorama? 
Could they also be made from scratch in photoshop using 32bit color? 
Is there a reason why people don’t seem to do this more often?
Cheers
Yes, it is possible to do this. If you use a tool like Photoshop in 32-bit per channel mode, any values less than 0 or greater than 1 should be usable as a high dynamic range values. I don't know that I agree with your contention that "people don't seem to do this". Given that the tools exist, they must be supporting some workflow.