There is no direct argument/guidence that I saw for "when to use them", but masked arrays { https://numpy.org/doc/stable/reference/maskedarray.html } (an alternative to sentinels in array processing sub-languages) have been in NumPy (following its antecedents) from its start. I'm guessing you could do a code-search for its imports and find arguments pro & con in various places surrounding that.

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.