It has nothing to do with them being “rigid”.
In Chinese tone is part of the way the spoken language differentiates between difference words.
Take the “Shen” of “Shenzhen” for example, in tone 1 Shen can mean the verb “to Stretch”, in tone 2, Shen is a noun, it means “God”, In third tone, it a verb “to Judge”, and 4th tone, it’s a verb “to seep through”.
The same “Shen” to you can means things that are vastly different when pronounced with different tones. That’s why without the context of “near HongKong”, when you prounce it in the wrong tone, it can prove very difficult for someone decipher your meaning.
I understand that Chinese is a tonal language. I also work very hard to pronounce things(what limited words and phrases I know) with the right tone. My point is that if something isn't EXACTLY correct, it doesn't mean the same thing. This leads to binary thinking. It means that as children, they spend a lot of time reciting things, exactly. It means they copy things very well because that is how they must learn.
In my particular case with Raymond, our driver, he asked me where we went. He knew we went somewhere. My poor toning of Shenzhen should have been decipherable. It was not. That was just one example, I've been dealing with native Mandarin speakers and some Cantonese for over 15 years. It's something we've become accustomed to. We tend to just text or email when they don't understand and they run it through a translator and then they get it.
Ah, languages, one of my favorite topics. For the moment I will talk about Spanish. Spanish has 4 forms of you—tu and vosotros (seldom used) for thee singular and plural; Usted formal singular, Ustedes formal plural. It has two verbs for “to be”—ser and estar. Ser for permanent states—I am a man, estar for temporary states—I am tired. More difficult are the two categories of verb forms—Indicative and Subjunctive. Indicative is something which actually is—I came to school (I actually did that). Subjunctive—Come to school (this may or may not happen and takes a different verb form. In Spanish almost half of the sentences with verbs are subjunctive—that is, things might or might not happen. Germans don’t have that problem, most things are very certain. The Romance languages, and it seems often the people have the more uncertain quality based on the subjunctive. A rare English form can be seen in “If I were king.” versus “When I am king.”
I took a linguistics class in Mexico and we studied a little Aztec (Nahuatl). They have a form called an “infix” while we only have prefix and suffix. I want to eat tortillas can be written: Nicnequi nicua tlaxcalli or Nicnequi nitlaxcalcua, or something like that. I took the course 50 years ago. But I have not seen that in germanic or romance language forms.