I don't follow...sure, a lot of research is medically inspired, but that threads off plenty of research into the entirety of the workings of cells. I'm right now reading about kinetic studies of protein folding as a factor in formation of protein aggregates, which may or may not be linked to a number of diseases, including ALS, Alzheimer's, and drug resistance. Then you have entire pathways of metabolism being studied to aide in nutrition and obesity studies (And vice versa).

only specific genetic diseases are caused purely by a gene being out of whack

Sure, but you still have larger categories that can be slightly more distantly linked to general diseases. (Ex: Tumor-suppressor genes and cancer)

NIH wants logic, technical ability, and sensitive measurement, without much regard for utility.

This is where you've lost me, does medical application or biosynthesis not count towards utility?

If you want an actual specific example, go to PubMed and just start taking a peek around.

Citing one would be preferable, I'd say that the majority of the microbiology papers I've read thus far made sense in some context or another. Some's shite, but higher tiered journals are generally a little better at filtering for that, and who am I to judge if someone's research is worthless? :P