They got the object level way wrong

So your above comment considers abolition a "currently acceptable dogma"? That doesn't seem true, it's still well out of the Overton Window.

The article isn't doing analysis as much as advocacy, but it isn't really trying to convince. Its purpose seems to be to motivate people already convinced to actually do something, or to spread awareness of a position (again, without arguing for it). Both are valid, and complaining about it not being rigorous enough seems to be missing the point.

However, it fails to note that that implies that something must have occurred over the last 40 years that caused this explosion and thus the solution should involve figuring out what changes have lead to this explosion and undoing them.

The obvious answer is "drug laws and mandatory sentences", and the article does propose to do away with them.

Also, the specific proposal is

 Abolition would end the death penalty and life sentences, and push the maximum number of years that can be served for any offense down to ten years, at most.

which is (as the article fails to mention but should have) similar to some European countries, so can't be too terrible.

Later the article quotes Tony Papa of Drug Policy Alliance, and says he spend 12 years serving an "unjust sentence", but fails to specify in what way the sentence was "unjust". Was he wrongly convicted, if so the problem is that and not the existence of minimum sentences. However, one gets the impression from the authors lack of interest in the question (or for that matter in what crime Tony Papa was incarcerated for) that the use of the word "unjust" is BS in Frankfurt's sense.

Not mentioning something doesn't mean lack of interest. He's mentioned as being from the Drug Policy Alliance, and sure enough https://en.wikipedia.org/wiki/Anthony_Papa

15 to Life, published in 2004, is an autobiographical account of Papa's experience with the New York criminal justice system and anti-narcotics laws under which he was sentenced to fifteen years to life imprisonment for a first time drug offense.

The unjustness is clearly the belief that drug laws are unjust, which is also something the article takes for granted and assumes the reader does as well.