The theorem is particularly simple to prove for a constant force acting in the direction of motion along a straight line. For more complex cases, however, it can be claimed that very concept of work is defined in such a way that the work-energy theorem remains valid.
I understand what you're saying, but...
In The Feynman Lectures on Physics, Volume I, an exploration of torque produces a motivation for the definition of the vector (cross) product. I think there is a similiar procedure with work, but I don't know why work is defined as a scalar. The work-energy theorem in one dimension is not useful for this, and I don't know what else to use to show that work is a scalar.