The tonal speaker hears a much wider and more precise range of tones, but that precision also kind of hinders them in a way because they can't not hear it. On the other hand speak with a tonal native speaker who's also learned a non-tonal language and they can understand your mistakes (in their native tongue) perfectly, because they essentially have already untrained the tonal instinct. But I'm sure hearing those tonal mistakes feels quite jarring to them nonetheless, like when you're listening to a musician who gets a chord wrong - it just hurts.
The native English (many other Indo-European languages also have similar systems) speaker is very unlikely to make a pronunciation mistake in this manner but even very accomplished francophone speakers of English struggle with it even after being corrected.
For example here’s French cabinet minister Bruno Le Maire pronouncing “damages” as “daMAges” https://youtu.be/qKWFsg5uHKo
I learned this is especially valuable when switching between instruments with different constrained ranges (you can just adapt), as well as your voice changing over time.