Did market power go up so much?

It seems not:

De Loecker et al. (2020) (DEU) estimate that markups increased significantly in the United States from 1955 to 2016. We find this result is sensitive to unreported sample restrictions that drop 27% of the available observations. Applying the methodology as described in the article to the full sample, markup increases are more muted until late in the sample period, and are almost entirely driven by Finance and Insurance firms. If these firms are removed, markup increases are modest. We conclude that the DEU methodology and data, as they are described in the article, do not support the conclusion that broad-based increases in market power have occurred in recent decades.

That is from a recent NBER working paper by Benkard, Miller, and Yurukoglu.