Tapered head tubes - why?

There is a growing trend for so called tapered headsets in road bikes.
The reason given being increased rigidity.
This seems to me to be a solution to a problem which does not really
exist. I have a year 2000 Shwinn Peloton with the original fork which
has a 1" steel steerer tube. I am 6'4" and weigh 200lb, I don't race
but I like to think I ride pretty fast. Yet I have never been aware of
any problem with flex around the front end of the bike even when
cornering at 60+ kmh. Many new road bikes now seem to have head tubes
which are beefier than my mountain bike which has given years of
trouble free service.
I would have thought flex would be concentrated at the midpoint of the
steerer tube of the fork rather than the frame itself. If so why not
just beef up the normal 1 1/8" steerer using the now common super
dooper stiff carbon fibre in order to increase rigidity rather than
introduce a new standard or rather combination of standards?

Is the tapered head tube idea even valid in engineering terms?
If so is it really relevant to the humble road bicycle?