One problem with this argument is that “British English” itself includes so many vastly diverse dialects. Try reading Irvine Welsh and tell us it’s barely different to American English!
It’s true there’s often a large degree of levelling between “standard” written languages, but that doesn’t mean there aren’t strong distinctions in the dialect. Dialect has an awful lot to do with how people actually talk, not just how they write.
(Also, I don’t think dialect actually excludes accent, rather accent is just one of the many features that makes up dialect.)
Please note that the categorization of certain languages as the hardest to learn by the Defense Language Institute, the Foreign Service Institute, the British Foreign Office, or other such government offices that are concerned with teaching them to adults for job purposes applies only to the languages that they care about. They don’t bother to categorize, say, some Australian aboriginal language with only about a hundred speakers left.
North Islanders from South Islanders not so much, but Southlanders from the rest of the country yeah…then there’s the JAFAs, who while they don’t sound different, only another JAFA actually wants to talk to them.
Speaking serioulsy though, not sure what it takes to qualify as another dialect, but definitely there are many localised usages that would not be understood outside of their respective countries. Also I KNOW (but can’t remember and don’t have to\ime to research which) Australian in particular has some participles that are different to standard “QBE”
And of course Australians have that whole sibling jealousy going on - you know when the better looking, more intelligent brother gets all the girls, so Australians regularly try to make New Zealanders look bad
