What doesn't help is implying that one would want to shoot a full frame at the same exposure as a crop body.
Did I imply we'd want to? I didn't mean to. I was just providing the usual basis for comparison.
That's as helpful as suggesting that you would use the same focal length.
I agree that we often want to use different exposure settings on different formats. That's worth pointing out. With the smaller sensor we more often cannot use the settings we'd like to. You already pointed out the smaller format's frequent inability to produce as shallow a DOF. There is also the matter of smaller formats not having equivalently low ISO.
For instance if we wanted to shoot on the 7D II to get the same DOF, framing, motion control and noisiness as we got on the 5D III using an 85mm lens at f/1.4, 1/1,000, we'd want to shoot a 53mm lens at f/0.875, 1/1,000, but such a fast lens doesn't exist.
If we wanted to match on the 7D II a SOOC JPEG with about the same image lightness, DOF , noise control, and noisiness as one we took at 80mm, f/2.8, 1/500, ISO 100 on the 5D III, we'd want to shoot at 50mm, f/1.8, 1/500, ISO 64, but that ISO isn't available on the 7D II.