I agree that new divers are best off getting a computer, in fact I think getting one was one my earliest post-certification purchases; at that time they were a little more expensive, but you could still find deals.
But, I have to take issue with the idea that a dive computer is a potentially life saving piece of equipment, at least for a new diver. I can sort of see the idea in theory, mostly due to ascent rate alerts helping to deter an uncontrolled ascent. But new divers are very unlikely to have NDL issues unless they are diving far more aggressive profiles than is the norm, and generally new divers are not very good on air, so they end up with generally shorter dives. That's not always the case, but it's typical.
What I do think is potentially life saving for new divers is some basic knowledge of how dive behavior affects DCS risk and learning to dive accordingly. A computer can help with that process but it's not at all necessary.