My observation would be, from an appropriate restoration perspective (or reconstruction point of view) Dave's initial observation shared above is very accurate.

If a given region does not present in its historic timber frame architecture the evidence of adz work, then with regards to the given ethos of..."like for like, in means, methods and materials"...the use of an adz would be an unwarranted system, and out of context for said work.

In general, regarding adze work itself...my experience and observation would be it is both a regional, cultural and time period based matter. For some regions and cultures, adz work is the primary finishing method left on timber and plank, with perhaps further refinement with a planning methods within a given wood culture's practice. In other regions (as Dave has shared) the axe (in one of its various forms) is the only system used to shape and/or finish large timber.

Another perspective on the subject, would be the apparent fact, that if adz work was not a common event within some regions, and/or at some time or place in history, then there would not be as many of the tools left in collections as we can find in some areas. Clear evidence that they were employed extensively at times and in certain places...