Special values like NaN are half-assed sum types. The latter give you compiler guarantees.
From memory, I have heard "infecting all downstream" as both "a feature" and "a problem". Experience with numpy programs did lead to sentinels in the https://github.com/c-blake/nio Nim package, though.
Another way to try to investigate popularity here is to see how much code uses signaling NaN vs. quiet NaN and/or arguments pro/con those things / floating point exceptions in general.
I imagine all of it comes down to questions of how locally can/should code be forced to confront problems, much like arguments about try/except/catch kinds of exception handling systems vs. other alternatives. In the age of SIMD there can be performance angles to these questions and essentially "batching factors" for error handling that relate to all the other batching factors going on.
Today's version of this wiki page also includes a discussion of Integer Nan: https://en.wikipedia.org/wiki/NaN . It notes that the R language uses the minimal signed value (i.e. 0x80000000) of integers for NA.
There is also the whole database NULL question: https://en.wikipedia.org/wiki/Null_(SQL)
To be clear, I am not taking some specific position, but I think all these topics inform answers to your question. I think it's something with trade-offs that people have a tendency to over-simplify based on a limited view.
That's fair, I wasn't dimsissing the practice but rather just commenting that it's a shame the author didn't clarify their preference.
I don't think the popularity angle is a good proxy for usefulness/correction of the practice. Many factors can influence popularity.
Performance is a very fair point, I don't know enough to understand the details but I could see it being a strong argument. It is counter intuitive to move forward with calculations known to be useless, but maybe the cost of checking all calculations for validity is larger than the savings of skipping early the invalid ones.
There is a catch though. Numpy and R are very oriented to calculation pipelines, which is a very different usecase to general programming, where the side effects of undetected 'corrupt' values can be more serious.
Anyway, this topic of "error handling scoping/locality" may be the single most cross-cutting topic across CPUs, PLangs, Databases, and operating systems (I would bin Numpy/R under Plangs+Databases as they are kind of "data languages"). Consequently, opinions can be very strong (often having this sense of "Everything hinges on this!") in all directions, but rarely take a "complete" view.
If you are interested in "fundamental, not just popularity" discussions, and it sounds like you are, I feel like the database community discussions are probably the most "refined/complete" in terms of trade-offs, but that could simply be my personal exposure, and DB people tend to ignore CPU SIMD because it's such a "recent" innovation (hahaha, Seymore Cray was doing it in the 1980s for the Cray-3 Vector SuperComputer). Anyway, just trying to help. That link to the DB Null page I gave is probably a good starting point.