Navigation flight planning during training

This question is directed at student pilots and flight instructors.

How many of you learn/teach cross country navigation using the
traditional methods using paper charts, protractors, E6B and
navigation logs?

During my training more than 10 years ago, xc planning was a fairly
elaborate process that involved filling lots of numbers in small
boxes. The flight was broken down into approximately 25 mile legs, and
each row had distance, true course, winds, temperature, variation,
wind correction angle, magnetic heading, time, fuel. Then we add up
the columns to get total time and fuel. We also compute the time
required to climb and descent. If we want to be more precise, we also
compute the fuel needed for taxi and run-up. Once airborne, we
religiously write down more numbers at each checkpoint and recompute
ground speed.

All fine, but I don't do any of these on a typical flight. I use an
online source such as skyvector.com to view the charts. Then I use an
online software to compute heading and time. That plus a paper chart
is pretty much all I need for a VFR flight.

I've been toying with the idea of taking a different approach to
teaching flight planning by skipping a lot of these things. I don't
see the purpose of doing things by hand when it is done much easier on
a computer. It feels like using a typewriter instead of a computer. In
addition, the less stuff you have in the cockpit, the simpler the
organization becomes. All these papers and pens flying around the
cockpit becomes an organizational nightmare.

So what are your thoughts on this? Is the ability to compute a flight
by hand really important? Are there important aspects I am
overlooking?