I've written and deleted and rewritten several long responses here and now I'm getting frustrated - maybe I'll come back and finish going over your questions later, but for right now...
I think the issue may be one of dealing with differing principles/versions of Bernoulli's equation. There are more advanced versions of Bernoulli's equation/principle (not developed by Bernoulli) that deal in compressible flow and that may be what you are describing. However, there are a couple of problems here:
1. A waterfall (or white water rapids) has no continuity - no streamlines. It can't, under any circumstances, be considered an application of Bernoulli's principle. Friction, viscocity, and potential energy dominate, and these are not adequatly covered by Bernoulli's principle in any of its forms. In particular, since it is open to the air and static pressure never changes, there can be no compressibility effects (even assuming water was more than a little compressible!).
2. In a venturi tube, air does experience compressibility effects that become relevant above about 220 mph. These compressibility effects result in ideal gas law implications for the flow: change in temperature with pressure/density changes. But these effects are explicitly excluded in the standard form of Bernoulli's equation: the flow is assumed to be incompressible. So when you say:
To me, "an idealized Bernoulli case" is the one Bernoulli derived and it explicitly discards the effects you are describing. Some of what you are describing is valid for more advanced versions, though. Read the wiki on Bernoulli's principle, paying specific attention to the descriptions of the two forms they describe: the compressible and incompressible flow forms.Please consider it to be an idealised Bernoulli case...