To add to the other answers, English is also pickier than most people realize when it comes to your pitch. [It’s not tonal within words, but it usually is within sentences](https://englishwithkim.com/pitch-tone-stress-intonation-english/). When the melody does not mesh with the expected sentence pitch shape, it will sound strange to native English speakers, and is often taken as a sign of a songwriter who is either non-native or a poor writer.
So even in English, the pitch must be accounted for in the writing–this is not necessarily unique to tonal languages.
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