> Someone from Shanghai will be able to speak to someone in Chengdu with their own dialect, just slower.

This is definitely not true (if they were to use their own dialect).

I'm from the same region surrounding Shanghai and although there are some intelligibility between dialects, it is hard if not completely impossible to have a conversation even between people from adjacent towns. See https://en.wikipedia.org/wiki/Wu_Chinese

I'm a bit surprised about your claim. Anyone from China with a sense of the dialects of the south would know this.