I believe students must be guided by intuition in a first year calculus course.

Therefore, it is better to use geometry to explain derivatives in terms of tangent lines and geometric limits of pushing points together. A student cannot appreciate the need for rigor if their intuition is not first sufficiently developed.

Since the MVT is mostly useful for rigorous computations, notably for the proof of the fundamental theorem of calculus, I agree that it is out of place in an ideal introduction to calculus.

My main objection is that it is a long side track to prove, and it seems pointless to a student who doesn't appreciate rigor, which is likely to turn them off to mathematics.

Furthermore, The fundamental theorem can be argued for intuitively by discussing the geometric ideas behind integration. When the student is able to see the flaws in the intuitive argument, they will also be able to appreciate the MVT.