Where I train, our teacher usually calls out for freestyle techniques starting at nidan. He'll usually ask the candidate to show one or two techniques from a particular attack and then he'll let the candidate do jiyuwaza with that attack. I think we do freestyle tanto, jo, and bokken attacks (and freestyle responses, of course) at sandan. Our yondan exams are the same kind of thing, too.
I've also seen tests (usually sandan exams) within our organization in which the testing instructor called for the person being tested to take his uke, treat him or her as a beginner, and show how he would teach that person how to do a particular technique. Sometimes, he asks that the person being tested not speak while doing this, too.
However, I will concede that most of the tests for dan ranking that I've seen (probably close to a hundred now) have been pretty much the same old "now, please show us yokomenuchi iriminage" kind of exams. Sure, different organizations have different emphasis (eg kumitachi and kumijo in some aikikai affiliations, ki testing and taigi in Ki Society dojo, kata in Tomiki-based places), but it's usually not that much different...