We teach calculus because it's a prerequisite for many scientific and engineering careers. It's not a mental exercise, it has direct, practical use for many types of scientific and engineering disciplines.
We can argue whether people actually use calculus in their everyday lives (I would argue so but it's maybe overly broad) but I think the best reason is because it teaches us how the world works and has direct, practical utility for a variety of fields.
On the other end, if the best argument really was that it was good 'mental exercise' then why not teach sudoku in class? Or minesweeper? Why not have people do a crossword puzzle for their final exam?
We want education that has enriches and enables students, not mental machinations for the sake of it.