Are sectional paths correct across "long" distances?

Awhile ago I pointed out in rec.aviation.piloting that one of my
tools will generate a map using stitched sectionals for a given
route.
http://groups.google.com/groups?hl=e....edu.au#link10
Ben Jackson mentioned that it didn't look correct to just draw a
straight line between two points so far away (across multiple
sectionals). I have looked into it a few times but I haven't
come up with a definitive answer.

So...anyone know the answer? Pilots are certainly accustomed to
drawing straight lines on a sectional to find the shortest path
between two points, and I've never been taught to do anything
other than align sectionals by sight to plan multi-sectional
flights. Does this not work over long distances?

One path I know fairly well is LAF-MER. The Great Circle path
happens to go right near Denver (where I usually stop). If that
path is plotted as a straight line on the sectionals
https://aviationtoolbox.org/Members/...selected.x=411
it appears to follow the path I'd expect.
https://aviationtoolbox.org/Members/...selected.x=427

Also, there's an easily-identified area on that path where Iowa,
Illinois, and Missouri meet. Take a look at the Great Circle
route.
http://gc.kls2.com/cgi-bin/gcmap?PAT....380N+120.568W
Again, this seems to match the area on the straight-line path
drawn on the sectional.
https://aviationtoolbox.org/members/...selected.y=324

Anyone know for sure whether or not this is an accurate way of
depicting Great Circle paths in the conUS?

Thank you.

--kyler