Louis, here are some reasons why I think it could be useful to stress test a system. It's probably less usual for a person who buys an off the shelf pre-made system to want to stress test it (one may assume that the manufacturer should have done this already), but for a self built system it's something I would always do.
1) To test stability. A stress test will reveal an underlying stability problem in hours or less, while the same stability problem might take a long time to reveal itself in normal use. But the thing is, they generally do reveal themselves eventually (as random crashes or shut downs when doing certain tasks, for example).
2) To test cooling is sufficient. Yes the tests artificially apply an extreme workload to the part you are testing. It's arguable that no real world software applies load in the same way as the Intel Burn Test and Furmark do (which are purpose designed to stress the components). However you can have some confidence that if temperatures are kept under control with those running, it should stand up to anything that normal use can throw at it. Just putting a system together, installing Windows and looking at the temperature from your desktop will give no clue whatsoever as to what sort of temperatures it can get to when asked to work hard. Video encoding can be a fairly high stress use (Handbrake encoding for example runs my CPU nearly as hot as Prime 95).
3) To test overclock stability. Obviously overclocking is pushing a part beyond it's rated performance. Overclocking may involve pushing a part beyond the level where it's stable, which varies on an individual component basis, and it's important to find out if you do this. You can argue that over clocking is unnecessary for most people, and I'd agree, but some components are marketed with ease of over clocking as one of their benefits - AMD Black Edition and Intel K processors for example. They are aimed at people who want to overclock.
4) Controversial one. To "set" thermal interfaces, e.g. thermal paste between processor and heatsink. Some argue that heating and cooling cycles are necessary to achieve full cooling performance. If you think it helps then fine.
At the end of the day it's a pro-active approach rather than a reactive one.