Internships and their bearing on securing tenure track faculty positions
In my field of study (software engineering, distributed systems), industry internships are also exceedingly common. So common, in fact, that I would also assume without having ever actually checked that a majority of young tenure-track (TT) faculty in my fields also did internships during their PhD.

Yet, I would argue that what you observe is a classical case of correlation versus causation. Yes, TT jobs and internships are likely reasonably strongly correlated, because:


Internships are high-profile and the best PhD students (AKA those that are likely to go on to TT positions) are much more likely to get one than weaker students.
Internships are, at least in my field, often insanely productive for the student, leading to one or multiple papers of highest quality. Obviously, having one or more A+ papers (more) helps a lot when you are on the job market.
Internships establish very tight connections to one or multiple, often well-known, industrial researchers, who can write strong recommendations.
Another somewhat indirect advantage is that the close connection to industry experienced in an internship helps people get new ideas and grow as researchers, hence leading to better papers and research statements once they are back.


However, this is not to say that search committees value the internship itself. If you were on an internship, but you were pushed in by your advisor, there was no paper, you did not learn anything useful, and you did not make useful connections, then the internship will not meaningfully help you get a TT position. Conversely, if you never did an internship, but still have good connections to the community and have written great papers regardless, the lack of an internship should not hold you back.