I was expecting Mandarin to be an exception, since the language uses pitch to encode different words; apparently it isn’t, the speakers simply “abstract” the phonemic vs. syntactical pitch variations as two different things, when interpreting the sentence. Check figure 6.

And while there is a particle overtly conveying “this is a question”, ⟨吗⟩ /ma⁰/ (the “0” indicates neutral tone), it seems that you can couple it with an assertive phrasal pitch to convey rhetorical questions. And other languages (like e.g. German and English, that overtly mark questions with verb fronting) show a similar pattern.

I also found some literature claiming that it might be cross-linguistically consistent

The most important observations are the following:

1. pitch tends to decline from the beginning of an IP [intonational phrase] to the end, a tendency known as declination;
2. the beginning of an IP may be marked by a local sharp rise in pitch or “reset”;
3. in IPs that are utterance-final and/or in statements, there may be a local drop in pitch at the end of the IP in addition to any overall declination spanning the IP as a whole;
4. in IPs that are in questions and/or are not utterance-final, declination may be moderated, suspended or even reversed, i.e. the overall trend may be less steeply declining, level, or even slightly rising;
5. in addition to exhibiting reduced declination, non-final and interrogative IPs may also have a local rise in pitch at the end, or at least have no local drop.

The validity of these observations, as general tendencies, is not in doubt.

The article also lays out some potential explanations for this. The basic gist of it is, nobody knows why but everyone has a guess.