This logic does not necessitate Mars ever being more habitable than Earth. Imagine one of the countless doomsday scenarios - a large asteroid impact. What kills you is not necessarily the asteroid, but it flinging debris into the sky that blots out the sun, not only creating a massive cold, but also rapidly killing all plants which starts a rapid series of extinction events on up the food chain.
If that happened Earth itself would still, even during the extinction event, be a dramatically more pleasant place than Mars. But nonetheless that event would kill off the overwhelming majority of people on Earth, and very possibly 100%, because it's such a significant change from the status quo we expect to continue on Earth. But having a parallel society or societies would ensure that even in the 100% scenario, life could get back up and organized relatively quickly. And even in the "only" 99% of people killed scenario, the outside help could help to reestablish order and kickstart society.
You could build a better 'colony' on earth to survive that event for way less money/effort/risk than a colony on mars. You aren't going to have a colony on Mars contributing back to the home planet in any meaningful way, and 1% of people left on Earth is still 80,000,000, many more than will be in a Mars colony.
> You could build a better 'colony' on earth to survive that event for way less money/effort/risk than a colony on mars.
How though? Not in terms of engineering, but in terms of politics and economics. The biggest charter city in the world just got ruled illegal and Honduras is about to take their stuff. Building colonies in Antarctica is forbidden by treaty. And much like Thoreau's cabin in the woods, if you try to make a self-sufficient colony somewhere that's not actually isolated, you might think you've succeeded but actually have been cheating all along.
Yes, objectively there are better options, just as e.g. ITER could have been built a lot more efficiently if most of the countries had agreed to pay one country to make it, instead of making precision parts in a bunch of different countries and having to assemble them together. But engineering and politics are the art of the possible.
Building colonies in-planet that could survive all possible scenarios would probably be impossible. But even if it were you'd face a pretty simple problem - who would ever want to live for there? You'd likely end up living in conditions that would make life on Mars look pleasant, without any of the upsides that might take people to Mars - adventure, ideology, commercial aspirations, perhaps even religious (you know the Mormons will want a planet or two), and of course 0.3g!
And who knows what the future holds in terms of population sizes? I also strongly disagree on the colonies not being able to engage in exchange. For a silly but very practical example sports in 0.3g are going to be insane. Jordan could jump something like 11ft and stay airborn for several seconds on Mars. That's going to be just be stupidly awesome to watch and play. MMA will look like a something out of a Chinese martial arts movie. For more mundane things, as the price of shipping cargo decreases the number of things available for trade increases. For example wine made in 0.3g will taste very different. Whether that's better or worse is yet to be discovered, but obviously such ideas will have no difficulty finding a market.
For better or for worse Mars (or the Moon) will also probably make amazing retirement places, especially if we can work on the scenery a bit. Taking that load of old bones might not only provide comfort but even increase longevity enabling a weaker heart to keep pumping a bit longer. And so on endlessly.
If that happened Earth itself would still, even during the extinction event, be a dramatically more pleasant place than Mars. But nonetheless that event would kill off the overwhelming majority of people on Earth, and very possibly 100%, because it's such a significant change from the status quo we expect to continue on Earth. But having a parallel society or societies would ensure that even in the 100% scenario, life could get back up and organized relatively quickly. And even in the "only" 99% of people killed scenario, the outside help could help to reestablish order and kickstart society.