This is such a weird statement. It's less than five times three very large areas combined... It leaves me with no idea how large it is. For those curious, it's about the same land surface area as earth has (removing oceans).
They've got the same challenges but are easier
Mars has 0 people living on it, and is already uninhabitable. We literally cannot make it worse for anybody, and are in no danger of wrecking anything we need to survive by trying.
I would much larger we try planet-scale geo-engineering on Mars, then try planet scale geoengineering on Earth (and we're already flirting with that because of climate change).
There is a wealth of information to be gained from attempting dramatic changes to a planet's condition, and establishing a biosphere, which would be extremely important for any attempt at large scale Earth biosphere repair.
How does it work?
* Do scientific research and exploration
* Win fame and prestige
* Enjoy having no existing property claims or cultural heritage to disturb
* No laws. Make your own laws. Escape persecution.
* Build a low light-and-RF-pollution observatory
* Create the ultimate off-site backup
Mars might not have regions that are better suited than these inhospitable parts of Earth but it has the feature of "not being Earth".
Consider it a backup/fallback for the "single point of failure" that Earth currently is not just for humanity but for all of life in the universe that we know of.
Now that we are developing the technical abilities to be able to remove this possible failure point and to finally add some redundancy for life, I think we are almost morally obligated to do so.
Mars also has fewer natural protections than Earth: a thinner atmosphere, no magnetic field to speak of, and no giant moon that deflects or absorbs at least some percentage of objects that would otherwise impact Earth. So Mars is more susceptible to dangerous radiation and object impacts than Earth.
For the same cost outlay (or way less) as trying to make Mars an effective backup for Earth Earth could be made more robust and dedicated purpose-built backups could be created.
Mars as a backup of Earth is like a cheap eBay thumbdrive hanging from a wind chime on your patio is a backup for your data.
What could happen to the Earth that would make it even close to as inhospitable as Mars?
It hardly matters that the apocalyptic Earth is more hospitable to human life than Mars currently is if we don't have any humans left to resettle Earth.
Even if a huge asteroid hit, we could almost certainly build shelters where more people could survive the initial impact than we can settle on Mars in the foreseeable future.
An analogy: a bunch of important files become corrupt (cataclysmic event) and the domain expert is no longer with the company (loss of knowledge and industry). It is much easier to move forward if one has a way of contacting a subject matter expert (Mars colony) to restore or rebuild what has been lost.
I believe we also need a colony to hold on to seeds of civilization in the very sense of the word.
It's like making a backup of your computer but never testing restore. The chances of that backup not being complete or recoverable are fairly high.
The backup of human civilization on Mars will probably be theoretically worse than one that can be made on Earth. But it will be supporting life, making it fully tested and thus practically better.
We might not colonize a neighbouring star system in the near or medium term future but I am convinced that if we do not start moving out into the solar system, we never will go anywhere else either.
Mars has no fossil fuels, so that can't be it. Minerals cant really be destroyed or exhausted. Technological knowledge is much easier to preserve from cataclysmic events on Earth than it is on Mars (if we fall under some kind of technophobic super empire that seeks to destroy this type of technology, that will as easily spread to Mars as to the rest of the Earth).
If our low earth orbit space gets too full of debris, we become stuck until we can find ways to clear it out.
But no doubt they will say: use broadcast power.
I'd like to see a system that, allowed to order any stock catalog item on Amazon or Digi-Key, could self-replicate.
Sure, temperatures would go down (but nowhere near as cold as Mars) and it would be hard to harvest plants, but we would still have fossil fuels to generate electricity for grow rooms, and we would still have earth soils that are ultra-rich in nutrients. The surface would be nowhere near as radioactive, so people could still work outside, allowing mines and so on to keep operating as today.
Overall, while it would be a huge tragedy, kill billions, and destroy our civilization as we know it, it would still leave the Earth as an absolute paradise compared to Mars.
If we were talking about another planet in another solar system, you could have some arguments about long term survival, but otherwise the earth will at worse become as inhospitable as Mars, until the sun burns them both to a crisp at about the same time in a distant future.
Similarly, any asteroid impact of a size that the Earth has seen since life appeared would neither wipe out ALL of humanity nor leave the Earth in a shape as horrible as Mars is in right now.
Edit: we know this for sure, because even after the asteroid that wiped out the non-avian dinosaurs, human sized and larger animals survived and thrived through the impact and fallback, despite having no access to any kind of technology or preparation. If the cold-blooded crocodiles could do it, I'm not worried about our chances.
Solar flares do not count as earth-ending events, at worst they could destroy our current electric networks and kill and strand maybe millions, but they are not in any way civilization-ending, nevermind life-on-earth ending as far as I know.
You also have a deep gravity well.
Land on Mars is free, there are zero taxes, no political system or unwanted populations.
There is no waiting for regulatory approval on a new building, no requirements to hire x % of your workforce as y demographic subset of the population. There is no national Government to negotiate with. Your population is completely comprised of high-IQ, motivated and skilled people, making for the best human gene pool of any place in the galaxy.
When SpaceX gets to Mars, it can simply... build, without limits. This is something not seen on Earth since the colonisation of the new world (which even then had native populations to contend with).
Until SpaceY gets to Mars. Then the absence of governments and regulation stops being an unmitigated benefit for SpaceX.