That's what we see in the data
Aren't search/trade costs a proxy for the market in question though? For example, suppose prior to the internet, you had two bookstores in your town. That was your relevant bookstore competition market. With Internet and delivery (lower search and trade costs), your relevant market is now bigger, basically the whole US.
So before, every town had two bookstores, thus nation wide competition would be seen as large (low concentration). But locally it would be a duopoly. Now with Internet, suppose we have Amazon and B&N, as the only bookstores. This is again a duopoly from the perspective of the town dweller.
Measuring market concentration change here is influenced by the relevant market changing, which means this is no longer an apples to apples comparison. You probably wouldn't have wanted the two bookstores (pre-internet) to merge at the time. One could argue that for the US the search and trade costs have been close to minimized.
I would be interested to also test the relationship to new entry decisions: if a market is very competitive and prices are closest to marginal cost then entry looks unappealing, therefore number of firms is monotonicly downward. If a market is less competitive then price will be well above marginal cost and lots of new entrants will show up, thus biasing the number of firms upward.