Yes time is limited, as I recall it was a question every 2 minutes. But we do not live in enlightened times as far as the JAA are concerned so electronic gadgets are the work of the devil. The only approved tool is the CRP computer so you will have to learn to use it like the rest of us.
It would indeed be easy to do the exams with the electronic version, just plug in the numbers and out pops the answer!
I do have a used only for the exams CRP5 for sale though as I much prefer my ASA computer for real world planning!
As for the tosh about batteries, show me a pilot who can do calcs on a CRP while keeping an aircraft sunny side up in IMC hand flying and I will show you an MS Sim Jock with a pause button........