"I have been frustrated by the lack of basic calculus and algebra skills that Harvard Calc taught students have. They are ill prepared for subsequent math courses."
I wonder whether David really means "calculus and algebra skills" as opposed to "symbolic manipulation". I find that students taught on the conceptual level of programs such as the Harvard Calculus are, in fact, more deeply connected to the basic concepts and purpose of calculus. The trade-off seems to be that there is a reduction in the students' abilities in applying the rules of algebra and trigonometry.
Perhaps we could look at this as an opportunity rather than a curse. I have found that students who come to understand and appreciate the concepts of mathematics are more often motivated to work to develop an understanding of the underlying structure that the concepts are built upon. I would expect an increase in the number of students who would look with favor on new courses designed to develop the skills that are de-emphasized in conceptual calculus programs.
I fail to see why calculus remains in the minds of so many as THE course that qualifies students as mathematically able.