That depends on the accent. I believe that's probably true for
the educated south of England, BBC, received pronunciation. I
don't think that's true for some of the other dialects from
northern areas (e.g. Liverpool) or the "cockney" accent.
I too have always wondered about this.
Since you've acknowledged that it's only the RP accent which gets that
respect in the US (and since I speak it, I rather enjoy my visits
across the pond) and others are either cute or obvious hicks, it
shouldn't be a surprise that the same applies to the wide range of
accents used by Americans.
The strong Appalachian accent of the guide who took us round some
caves in WV last year was the epitome of unsophistication - although
what he said was extremely informative and delved into some advanced
science.
My wife's an Okie, but she speaks the US equivalent of RP - the one
used by newsreaders on the main terrestrial TV networks and which is
commonly thought to be used mostly in Ohio and other places just south
of the Great Lakes. If there's such a thing as a standard "American
accent", that's it. It neither sounds dumb nor clever - just American.
Some of those sonorous slow talkers from the South, and majestic bass
African-Americans like James Earl Jones or Morgan Freeman, have far
more gravitas than any English accent can: to us, such people sound
monumental.
But most of the obviously regional accents in the US sound cute or
picturesque, while the ones Americans tend to regard as hick accents
just sound comical.
The problem which a lot of fairly-midstream American accent users face
is that it's the same sort of thing which Brits try and imitate when
they want to suggest a snake-oil salesman. At bottom, an American
accent doesn't mark someone out to a Brit as dumb or unsophisticated,
but the immediate suspicion generated is that they're a phony and
likely to be saying stuff without much regard for its accuracy.
Cheers,
Mike
.