I'm also amused by your remark that counterpoint is not taught in "the way it would've been understood by successful 18th-c. musicians." Most contemporary counterpoint instruction still follows the method of Fux's 1725 textbook (species counterpoint). Indeed, the fact that the pedagogy hasn't really changed for hundreds of years is often advanced as a criticism of current-day instructional practice!
> common harmonic sequences
Common harmonic sequences are not voice-leading schemata. If anything, the former are a side-effect of the latter. Even teaching cadences as a "harmonic" motion rather than a pattern involving the melodic motions of tenorizans (2^--1^) cantizans (8^--7^--8^) and bassizans (5^--1^) is a very flawed understanding that would've been quite foreign to 18th-c. musicians.
As for the thoroughbass, the older textbooks may give a cursory explanation of the notation involved, but what about the practice of it? Where is the règle de l'octave - the "harmonic" bread-and-butter of so much music of the common practice, known even to amateur accompanists back in the 18th c.? A lot of the time, it isn't there. And that's literally the simplest and most basic part, there's plenty of more involved patterns that musicians back then would've known in some way.
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.