Famously there is no consensus of how to interpret the equations of quantum mechanics, which naturally restricts introductory discussion to the mathmatical aspects.
I'm not sure why do you mean by "introductory discussion" but I think "popular science" books focus mostly on the controversial parts. At the university level, at least in my experience, you study a lot of classical physics, early quantum physics (1900-1925), and mathematical physics before taking a first look at Quantum Mechanics (Schroedinger/Heisenberg). And you may never be exposed to the relativistic extensions.
In contrast a textbook about thermodynamics will be all steam engines at the start, or maybe talk about a thermometer. Solid, sensible things and no talk about Gibbs free energy or any of the deep theory that exists.
You could start a QM book talking about the double slit experiment, but would have to write a lot of "one interpretation" and "some views say this". Or you could just brazenly pretend there is no controversy and make every reader that knows of it very suspicious indeed.
That is indeed how my favorite QM book starts: Cohen-Tannoudji. See also Landau for one that starts from experiment and not theory.
In any case introductory books that discuss the physics and not just the mathematics do also exist, like vol 3 in Feynman’s lectures.
Edit: I’m looking at Griffiths’ book and after defining Schroedinger’s equation in section 1.1 he devotes three pages to discussing its statistical interpretation in section 1.2 and mentions different interpretations, the Bell inequalities and the measurement problem. He comes back to these philosophical issues at the end of the book in a 12-page afterword.
For a recent head-scratcher, though, see https://www.nature.com/articles/s41467-018-05739-8
I think it's much less interesting than it seems at first sight.
Related (and clearer): In Defense of a "Single-World" Interpretation of Quantum Mechanics (Jeffrey Bub) https://arxiv.org/abs/1804.03267