Why would you need a billion people? evidence surrounding the Toba catastrophe suggests that all 7 billion current humans are descended from just 20,000 people or so.
If Mars is terraformed, you move a few people there, and make sure they can reproduce until they make the population of Mars number in at least the tens of thousands.
I think you’re misreading the timescale here - if we terraform Mars, we’re talking about people in the 2200s or 2300s doing it, not really ‘us.’ It’s unclear what the resource-to-problem ratios will be in the year 2200, so I’m not going to fight XT’s hypothetical.
Good point - even so, there are other major disasters to insure against, everything from a super solar flare (like in Larry Niven’s Inconstant Moon*) to aggressively used spaceships (like in John Varley’s Red Lightning**) or a global pandemic (like in World War Z[sup]†[/sup])
But I suspect Stranger is right, and the utility aspects of terraforming would be superseded by hollowing out asteroids or building orbital rings. It’s still entirely possible terraforming of Mars would be just an aesthetic project undertaken by a civilization of almost unimaginable wealth at some point centuries in the future, though.
[sub]* As far as I understand it, these have not been shown to exist, at least in our Solar System
** Also not shown to exist - these are some really bad examples, aren’t they?[/sub]
[sup]†[/sup][sub]Yeah, I’m not really trying anymore, am I?[/sub]