The purpose of mathematics in a liberal education when it is not a prerequisite to other subjects

Suppose a calculus classroom is full of students majoring in Classical Greek or music or literature or sociology or pre-medical studies or any of many subjects that do not require the course as a prerequisite, and not one of them intends to take a subject requiring as a prerequisite any of the technical skills (finding derivatives, limits, integrals, etc.) that could reasonably be taught in calculus course, and every one of them has said so.

Should a syllabus contain something like the following statement?

• The purpose of this course is neither to prepare you to use your knowledge of calculus nor to provide you with an opportunity to show you can work hard and overcome difficulties and thereby earn a grade to impress future employers, graduate schools, etc. Those may be side-effects, but neither of them is the intended purpose. The purpose is to contribute to your education by acquainting you with one of the great intellectual, scientific, cultural, and aesthetic achievements of humankind and with the kind of thinking that is used in this field.

Two concerns about this (conceivably objections to it?) are:

• Most students have never suspected that there are other purposes than the two that this statement says are the purpose of the course. (In a reasonable system, they would find that out long before reaching calculus. The main thing that is unreasonable that differs from such a system is our current practice of pressuring or even coercing students known to be unqualified to take calculus to do so, anesthetizing ourselves by telling ourselves that the systems for screening out the unqualified actually work.)
• The usual syllabi say one must cover the following technical topics (computing certain limits, derivatives, integrals, etc.) within the allotted time: [insert list here]. The perceived imperative to cover everything in the list precludes many things that would help students understand. When I mentioned one such thing, I was told "It would be nice to include that but there's not enough time." I said "So scrap ninety-percent of the material and then there's time." I don't know if that was taken seriously. I don't of its being implemented anywhere. And the usual textbooks are for the sorts of students for whom it is reasonable to insist on covering everything in a list of technical topics.