Computers do not work at reduced efficiency if starved for
power. This made so painfully obvious even from a data sheet
for any simple logic IC.

That is so, but a computer is composed of many more components than the CPU.
Power supply problems can cause errors not so much on the CPU but with the
drives, for one.

What do you think will happen on a modern computer when the hard disk trips on
account of inadequate power?

Every component in your computer requires power to run. If the power supply is
unable to operate to the demands of the entire system, you will have problems.
While the CPU may be running hunky-dory, other parts may not run so well and
you can have crashes and hangups. In power, you've got to deal with volts and
amps, and both indicates watts.

Volts measure flow potential, amps measure current level, and watts measure
actual ability to perform work.

Here's something for you to check out:

http://science.howstuffworks.com/question501.htm

As for overclocking, pushing a CPU at a higher rate of oscillation will put
more strain on it. This effect is well documented.

Most every desktop system works just fine on a 250 watt
power supply.

Not if you are running a high end P4 system which requires more than 250 watts
and uses it's own dedicated power socket.

Bigger PSU is often a solution to failure by the computer
assembler - who failed to learn basic facts. Bigger PSU does
not make a CPU work more efficient or faster. Even concepts
in overclocking are being misrepresented.

A power supply that has a higher level of overhead helps the entire system run
without problems. Running a power supply that is insufficient for the demands
of the computer will strain it and the computer will not be reliable.

As for overclocking, all it's about is pushing the CPU and RAM to levels beyond
what the manufacturer had indicated. However, you need better cooling to pull
it off as you do operate them at higher bus and multiplier levels, which puts
more of a strain on them. - Reinhart