FWIW I’m not quite convinced there’s that much of a dialectical divide: “Not bad,” “he’s not wrong,” etc. sound entirely natural to me in American English.
In a scale of 0 to 10 where "bad" is 0, one side will take "not bad" as a 4~5 while the other side meant it as 7~8.
Especially compared to a language like German. I took 5 years of German and still didn't have a damn clue what anyone was saying if they were talking in dialect.