If anyone has made the observation earlier in the thread, my apologies.
As far as I can see, PBL has been pretty much a lone voice in the wilderness extolling the influence of M. Certainly chaps such as JF and MFS, naturally enough, will be well aware of the following ..
For routine activities we tend to think of lift and drag only being functions of alpha and that works fine and beaut for most low speed activities in typical aircraft.
However, for many circumstances one needs to delve just a little deeper to get the story. If one digs into any of the standard engineering texts, one finds that the variables include -
(a) alpha
(b) a length measure of some sort, usually taken to be mean chord
(c) density
(d) dynamic viscosity
(e) local velocity
(f) sonic velocity
If one plays with some dimensional analysis sums, and that's always good fun, this list can be simplified to CL and CD being dependent on
(a) alpha
(b) Re (Reynolds Number)
(c) M (Mach Number)
For most cases, we can ignore the effects of Re and M and simplify to the usual CL = etc...
However, if there is any significant variation in Re or M throughout the flight regime, then one ought not to be surprised if the simplified sum gives a dodgy answer ...
It's not helped by pilot training only talking about the simplified sum without qualifying that story with the usual engineering caveats.
As we so often find, a little knowledge can generate the most stimulating of spirited discussions.