I think an introductory course would ideally hop back and forth between the explicit execution of specific examples and the understanding of abstract concepts. As you say the concepts are very important - for example, the author never mentioned the associative, distributive, or commutative rules which apply to all cases of addition and multiplication (but not necessarily to subtraction and division). Those are universally applicable, and indeed understanding them is important for moving on to higher maths (group theory etc.)

However, without doing a fair amount of ditch-digging, abstract general theories of ditches might be hard to grasp. For a programming example, consider data structures - lists, trees, graphs, and so on. The abstract concept is clearly what allows larger constructs to be made, i.e. entire programs, but if you've never actually implemented a linked list in any particular programming language, and try to, the result is almost certainly going to be a buggy disaster.

The optimal math education might be one where for every hour the instructor spends on the conceptual approach, the student then spends about three hours on the execution approach as applied to specific examples of those concepts (ideally with a teaching assistant around to help if the student gets stuck).