Please allow me to share some of my views. I'm a native Mandarin speaker.

> I can guarantee that tones are not particularly useful and that you can communicate with native speakers with all the tones messed up, and that's perfectly fine.

Not at all. Tones are extremely important. If you have all the tones messed up, you can hardly communicate in Mandarin. It's true, as you said, that different regions of China have different dialects, and you'll find that people can communicate normally because: 1) The tonal differences in nearby regions are not too significant, and people can still try to understand based on context. And 2) In many cases, people switch to regular Mandarin when their dialects cannot communicate with each other. This is why Mandarin exists. It is an officially regulated dialect that all Chinese people learn, to solve the dialect problem among different regions. Chinese people may speak their own dialects at hometown, but when two Chinese people meet and find that their dialects cannot communicate, they immediately switch to Mandarin. Therefore, the tones in Mandarin are very important. To a considerable extent, Mandarin exists because of tones. You cannot communicate in it with messed up tones.