Well, the old way wasn't free.
Every hour, 7 days a week, an HGV full of paperwork turned up at a dedicated paper handling centre. And that paper was then processed, for around 30 million vehicles a year.
I can well believe it might have cost a couple of million a week to run. Or more.
They send me a reminder in the post, why should it cost any more to send out a tax disc instead ?
The online bit will remain online.