It sounds like the doctor is considering the steady-state issue, which is more than many seem to, but I do question that in a cross taper since it's the same class. It's sensible to consider not dropping too low before the new med is propping things up more.
The funny thing is, Ian, I've read the guidelines for this in the UK and cross tapering seems widely open to interpretation, which is not ideal with GP's. At least the OP has a plan that can be easily modified based on response unlike a full stop & start regime.