I have done quite a few consolidation tests on re-compacted soils. Mostly in-house, but was able to charge for some.
The main reason is to answer the question, how much will the fill, usually of moderate thickness, actually settle or heave? That is a question which is rather common on this board. I feel I have a very good handle on what is to be expected and therefore, I can provide better recommendations and write better specifications.
And yes, even "when you compact a cohesive fill it is to some specification (i.e. 98%DD) and therefore settlement shouldn't be an issue?" you often don't really know until you test. Actually, I assume that most fills will settle, hopefully less that the replaced soils.
As I deal with clayey soils, I have also seen inappropriate compaction specifications which actually created expansive fill beneath foundations, slabs & pavements. A couple of consolidation tests may have alerted the geotechs prior to writing the recommendations.