Again, I am confused by your claims. The species system taught by Fux is, as far as I recall, the exact same way that counterpoint is introduced in, e.g., Gauldin's "A Practical Approach to 18th Century Counterpoint." (Gauldin goes into much more detail on other things, but the approaches are consistent.)

The fact that the upper voice goes 2-1 or 7-1 and the bass 5-1 at cadences is one of the first things taught in a counterpoint class. The rule of the octave is in most theory textbooks. The first example that comes to mind is Laitz, "The Complete Musician."

You're right that these textbooks don't teach how to improvise an accompaniment from a figured bass, but I'm not sure that's a good use of time for a theory class.