How frequently do pre-tenured assistant professors switch institutions? It's interview season. I've noticed that many of the applicants in this round are already assistant professors at other institutions.

Is there any known number or record on how frequently (let's say, across North America) assistant professors who don't have tenure yet switch institutions?

The market is already incredibly competitive. The academic institution has spent thousands of dollars on hiring a candidate and wants to retain them. If an assistant professor goes to another school and gets hired, then what you might end up with is this cycle of highly-ranking candidates swirling around and leaving empty positions in their wake. Alternatively, one might presume that the hiring system must be inefficient if, in a competitive environment, a university is unable to retain its hires.

This article (and associated comments) for example, illustrates how many faculty have changed institutions for various reasons; I also know personally at least two assistant professors who left their original institution to move to a new one within the first few years of them being hired.

Depending on the answer to this question, I would have a number of follow-ups (Do schools hate it if you apply elsewhere, and would they fire you? How does a department react when a recent hire leaves? Why do people switch? Are applicants often successful? Do people switch more than once?) but I'll start with this first.
It does happen. But it's not that common. I've been on faculty search committees for a number of years now, and out of the hundreds of applications I've seen, it's very rare to see pre-tenure faculty from other institutions apply. If and when they do, it's because


they're worried about their tenure case
there's a two-body problem (this is in fact the most "reasonable" reason to move)
they have other reasons for wanting to move (location, opportunity)


But it's not a frequent thing. Because it's hard to do: clocks have to be negotiated, research programs have to be uprooted, students have to be moved (and let me not even start on the logistics of moving a family that might just be getting settled in the first place)