Lack of take home examinations in mathematics classes? Why are so few grades in undergraduate formal math classes in most US colleges based on take home examinations or papers, barring one or two research/self study class?

The formal math classes I am referring to are topology, analysis, number theory, and calculus etc.

The writing class in my college is based on a take home paper, but I do not see similar grading schemes in math courses in other US colleges.
The American system often favors testing over project-based demonstrations of learning in mathematics and other quantitative subjects. The reason for this, at least at my university, is that you cannot be expected to do original work until you have a significant foundation in the field, and this original work is often extremely time- and resource- intensive. Thus, you will often find that for the first several semesters, the vast majority of courses in science and engineering are assessment-based. However, once you have gotten a solid baseline of knowledge, you can do original work in your upper-level classes (some people might even say this is a signature of a good program). This is in contrast to many humanities classes, where most of the papers you will write are inherently original, even without a well-rounded background.