I agree completely with the importance of seeing vectors as unitary things,
not as a list of three numbers. It has been a Good Thing having students
write small computational modeling programs in VPython because it provides
the first environment we've had where students can compute with vectors
rather than merely with components, which helps them conceptualize vectors
in a more mature way. After specifying initial conditions in a specific
reference frame, the rest of the program is typically completely
coordinate-free.
That this experience is unusual was made clear to us in running VPython
workshops at AAPT conferences for physics educators, because many of them
were quite unfamiliar with actually doing calculations with vectors as
vectors and kept wanting to deal with components separately.