Intrinsic wrongness of inequality is basically argument #4 from your link. It's the idea that the split of wealth is just inherently unfair, not because of any bad consequence, but because of something being wrong with having wealth too unevenly distributed whether or not it actually has any bad effects.
Claims 1-3 from your link are claims of instrumental wrongness of inequality claims 1-3 from your link. They point at bad consequences (rich people will control the media, rich people will corrupt the government, rich people will have unfair advantages for their children).
As the author of the article you links points out: "In principle, these effects could avoided, without reducing economic inequality, through such means as the public financing of political campaigns and making high-quality public education available to all children". It's not that inequality necessarily must cause these consequences, it's that it will tend to under some (most?) given policy regimes.
I think I misunderstood your original comment...when you said that "Inequality is not per se bad" was incorrect, I assumed you were making argument #4, which I did not see debated hardly at all. Most people were making some variant on arguments #1-#3.
In which case, I would respond to you: Paul does talk about the bad consequences and bad causes of inequality, and claims that you should address those causes and consequences directly rather than attempt to limit inequality in itself. The argument against this has to come in some form of "well yes, in theory it's possible to limit the bad consequences of inequality, but in practice it's too hard because X and thus we should directly attack inequality".
I didn't see anyone really saying that, everyone seemed to believe Paul thinks inequality doesn't have bad consequences or that he thinks we shouldn't address those bad consequences.