No genuine pilot can pretend to be able to use the circular slide rule in flight, unless he has an autopilot.
And if he has an autopilot, he obviously hasn't had a total electrical failure, in which case why not use the alternatives to GPS e.g. VOR/DME/ADF or even (dare I say it) call up ATC and ask for vectors or whatever. Of course anybody flying somewhere for real will just refer to the 2nd GPS (which will be running anyway) and get on with the flight.
This stupid device exists for the same reason as you need to wear a certain kind of pullover when playing cricket, or wear a leather apron in a masonic lodge, or the soldiers guarding Buckingham Palace wear those silly high furry hats, etc - it's a great olde English (note: not "British") tradition which usefully separates the men from the sheep.
I am rather suprised it is mandatory at the JAA ATPL level, since no airline pilot young enough to be currently serving will have ever used one for real. In the commercial air transport world, this stuff went out with the sextant. I hope that nobody flying jets for real actually believes otherwise; I would be seriously concerned for my safety if they did.
The FAA doesn't require it in the PPL, CPL, ATPL and guess what, all these are ICAO compliant. To top this insult to our regulators, most of the world flies under FAA licenses!! I just hope the Daily Mail never finds out.
To answer the original poster's Q I would suggest learning it just enough to pass the exams, and sell it on Ebay immediately afterwards.