Safety pilots are usually there to take over if the trainee F/O is not able to cope with the flying (and also if the Captain drops dead!).
Rather than sitting in the back, they are also a third pair of eyes and ears on the flightdeck. The workload is going to be very high for both pilots, so having a third person adds 'safety' to the operation. Whenever I have been a safety pilot, I've usually looked after the paperwork, supervised the fuelling, done the walkround, ordered the coffee etc. Captain and trainee F/O get more of an opportunity to do what they need: instruct and learn.
After the first 4 sectors, when the safety pilot is released, the the new F/O can worry about the paperwork etc.