We don't know that (and the article is quite low on the quality scale expected from Guardian).
I speak three languages, and I don't see a reason to mix. Of course, you might be right, but also that's a one trick point. You will be called for being pretentious or just obnoxious.
But I feel like this article is about something else. We don't think in terms of words, we think in terms of phrases, and when we remember those phrases it's not just their literal meaning, but also the context, and this can include the accent they were heard in.
In the ideal world we'd just play the sample that we have in the head, but we don't have that yet.
It's taken a tabloid turn (not just in terms of the page format). It's got noticeably worse, even in the last 6 months. It's packed with "listicle" articles ("10 reasons..."), and it's moving rapidly to the right, politically.
But I think most of the time it's just seen as hip, interesting, an extra flavor (flavour?). I do this occasionally -- sprinkle a foreign phrase here and there in my native Czech when I see that it fits and the other party might get it. More if I'm drunk. Some of my friends do it as well, in some social settings a number of jokes could be foreign language references. On the other hand, some people find it infuriating, as you note.
/me a Brit; used to have a Canadian boss (from Ontario).
Canadian: What's that about?
Me: Yes, a big one and it sank.
Canadian accents are largely indistinguishable from the generic American "TV accent" aside from a few specific sounds and vocabulary choices. If you go into the Boonies of Canada you hear more distinctive ones, but those are more like regionalisms, you don't hear them as much in the media.
My limited experience is that differences inside these two countries (e.g. New Foundland accent to Winnipeg accent, or Texas to Boston) are way bigger than averaged difference between countries (i.e. Manitoba to Minnesota). Most "Canadian" English is broadly similar to most "American" English, especially the standardized TV / Movie kind.
Then splash in some Quebecoise and that will really diversify things. Much of rural Quebec may not even speak English altogether. But you can tell the difference between Quebec French and France French pretty easily, with the latter sounding smoother. I've never been out west but I assume that BC and Alberta is the most 'normal' of the Canadian differing accents.
If Linus Tech Tips is anything to go by, this tracks. All of their hosts have very "generic American" sounding accents. They are very very close to Washington state which doesn't have a strong accent in my experience. Contrast this with Minnesota or northern Michigan and how "similar" they sound to the stereotypical Canadian accent.
Linus has a bit of a Valley Girl sometimes and wholly acknowledges it.
I had an easier time communicating even in smaller towns in Quebec, where it seemed that most people were capable of speaking a little English, even if they spoke French all the time.
It's also interesting that it's always a "posh" British accent: nobody ever fakes Cockney or Scouse or something.
The article specifically refers to faking an "Essex" accent. The Essex accent they're referring to is basically a cockney accent, softened a bit. When East London was gentrified, from roughly the 70s, many East Londoners moved out into Essex.
*Dick Van Dyke has entered the chat*
There’s something endearing to me about working class and regional accents.
* Review films made in the past 2 decades (that’s roughly when I began noticing the trend). Invariably, an English accent is used to imply authority or superiority (of some kind). Why this is happening in American movie industry is unknown to me but that it has been going on is clear for me.
Source: Texan who has been close to Canada once by visiting New York City. I know a Canadian and wouldn't have known it if he didn't tell me.
Serious answer, we hear a lot more British in pop culture than we hear Australian or NZ.