It's true that a decrease in labor power has probably contributed to rising inequality. That's not what you stated though; "It's a factor" and "it's the most important factor" are separate points. If you read the study I linked, you'll see that in advanced economies globalization and the skill premium have had roughly the same or larger impact as changes in labor institutions (which is a much bigger category than just "union power"). Regardless, both studies only show effects after 1980, not before.

> The second point it makes is about the role policy-making plays, which of course is probably as important, but is intimately connected to the presence or absence of union power because who the hell do you think lobbies for those policies?

Organized labor frequently advocate for policies that benefit their members at the expense of non-members (for example, licensing requirements) with ambiguous or detrimental affects on inequality. You use the example of minimum wage, but that's an ambiguous example too; we have some evidence that a high minimum wage actually decreases total low wage worker earnings[1], but a small increase (at least in the US) would probably be beneficial. To quote from the study I linked earlier

"Stronger labor market institutions could increase unemployment rates, reduce the wage differential between high skill and low-skill workers, and affect the labor share of income. The overall impact on income inequality, however, can be ambiguous: they increase unemployment, which tends to raise inequality, they can reduce wage dispersion, which tends to lower it, and they increase the wage share, which can have an ambiguous effect on inequality"

To be clear, it might be true that a decrease in labor power would be associated with policy that increases inequality but that's a non-obvious conclusion.

[1] https://evans.uw.edu/sites/default/files/NBER%20Working%20Pa...