These idents needed to be able to be shown on demand, in the event of a breakdown in some other piece of equipment. They needed to be able to run for arbitrarily long periods of time. They needed to be shown many times per day during regular programming. And you couldn't just connect up a computer and stream mpeg video - you would need some sort of a device that could generate the TV picture.
TV was recorded on video tape and video tape wouldn't work for this application - it would need to be rewound every time you stopped showing it; it would wear out with continual use; it would have a fixed maximum duration.
Having a camera standing by pointing at the appropriate device, on the other hand, was relatively easy.
Most tv stations just pointed a camera at a piece of card. The BBC obviously had to go one better and use a crazy globe and mirror setup.