Do road bike shoes offer an increase in power transfer over mtb shoes if the sole is a similar stiffness? Is there an argument against the use of road shoes if your were planning on time trialling and criterium races?
It’s probably more a matter of pedal systems than shoes. High end shoes in both categories will be pretty good and stiff.

I can only talk about Speedplay Zero (road bike pedals) vs. Look Quartz and Shimano SPD. The Speedplay Zero have a much greater area, have completly free adjustable movement sideways (as far as the crankarms allow it) and no play, tilting etc. whatsoever. Other road bike systems will probably be similarly good.

Road bike shoes will probably be lighter and have more openings for air to come in.

The only disadvantage of road bike shoes is that it’s really almost impossible to walk in them and the cleats suffer much more wear from it.