Ask people if they want gun laws enforced, and they say yes. Ask people if they like it when prosecutors charge a guy with 30 crimes for committing one act of armed robbery, and many start singing a different tune.
In this case though, straw purchases _are_ the main crime and there is a real lack of enforcement for that particular crime.
Such a subcrime would be a "lesser included offense"; you can charge for both offenses, but you can't get a conviction on both of them at once.
What this discussion touches on is not multiplicity but unreasonable multiplication of charges (at least in my jurisdiction we call it that). The test here is not the logical question of whether one necessitates the other by definition; it's the factual question of whether the offenses are part of substantially the same transaction. For example, a prosecutor might charge perjury, fraud, and larceny, wrt someone swearing to some materially false fact and fraudulently obtaining someone else's property with intent to permanently deprive them of it. These three offenses are not subsets of one another, but are closely related; it isn't logically necessary to commit perjury to commit fraud, in the abstract, but in a particular case that might be the mechanism by which one commits fraud. In my jurisdiction, UMC charges can stay on the charge sheet (perhaps the jury finds guilt on one but not all?) but, if convicted of more than one, they are merged for sentencing.
if a straw purchased gun is used in a crime, I'd be surprised if it didn't get investigated.
Well, let's say the original purchaser happens to be suspected of a crime (completely unrelated to a straw purchase, let's say bank robbery) and during a search of that purchaser's house, federal agents find a receipt for a check with "Glock 19" written on the memo line, it'll get their attention [0]. Very likely scenario :)
Other than that, good old fashioned surveillance plus a getting a confession [1]. I've also heard ads on the radio for a tipline to tell cops about straw purchases. No idea how well that works, though.
0 - https://en.wikipedia.org/wiki/Abramski_v._United_States#Fact...
1 - https://www.justice.gov/usao-edpa/pr/philadelphia-woman-conv...
This is usually resolved by not adding the jail times for the crimes, but by doing MAX(a, b, ...) on them. Prosecutors will suddenly only care about the most important ones.