One of the things I notice when I come here is that the mid-atlantic accent comes out.
Accents are kind of funny, since they are basically memes in the inflection (rather than the 'cant') of how people talk. When's the last time you heard someone (apart from T) say 'mega'? It fell by the wayside, a bit like 'begorrah', and awesome words like 'prithee' (which is why prego is one of my favourite words in any language. It's Italian for "I am being polite". It's basically an artifact of accent, or inflection.).
At a fundamental level, people want to talk like each other, because they appear more successful by fitting in, and imitate the accents of people they admire. I used to get pulled up for subconsciously imitating the accents of the people I'm talking to, and I still do it. I attribute at least part of my success at work with my ability to do that (of course, now that you all know, my career is ruined). Some of the most 'charismatic' people I know are the best at impressions.
In general, when you interact with someone, you want the most interesting thing to be what you say rather than how you say it. Therefore, to take the example of going to a foreign country where it's expected that you speak the language, you don't want the fact that you're opening your mouth and potatoes are coming out to distract from the fact that what you're saying has a profound and inimitable brilliance to it (although I suspect I would encounter resistance to the idea from the lady at work who, with a theatrical wink, told me that I could "Just keep on talkin' in that accent, honey").
Accents are malleable, and amending your inflection or manner of speech slightly, so that you're not some sort of space alien is far from disingenuous or dishonest. On the contrary, it's akin to using business speak to grease the gears a little. But, that's a topic for another day.