Firstly, I think the point of the demo of loading that many integers into the array, was to get a good measure of the memory usage per array item; by making the array big small one-time overhead memory usage is washed out in the average.
As to why you would want to do that in real life -- if you have written a large system with accompanying libraries, objects, or other infrastructure, then even if you pass of some sort of calculation to background or crontab tasks, you still might want to use your PHP code. I do this for some of the Drupal sites I work on - I setup drush commands that will do intensive calculations like most-related-article and etc to run behind the scenes have the results cached.
The best solution would be to improve PHP's memory usage so that the benefits may be had on page loads as well. I suspect (but have little hard evidence) that the size of PHP code and data structures impedes performance as threads and processes get pulled in and out of the CPU.
A secondary solution would be to take some of the libraries out there for doing specific operations, like scientific commputing and numerical libraries, and make them available to your code as a PHP extension. Obviously that doesn't solve as many problems as fixing PHP does.