I love how you go "We can survive in Mars's arid environment!" and then deny we can survive on earth.
We can survive on Mars if we organize an effort properly. We can survive on Earth if we organize properly. It's just easier to organize a single colony than billions of people in nations with clashing interests.
Why? Two reasons:
1. Less people means people know each other better. If the entire population of a Martian colony was about 2,500 people, you'd probably know at least a couple percent personally, a large fraction by name, and most or all by face. You have next to no chance of even
meeting 99% of the Earth's population. When just about everyone knows just about everyone, there's fewer people that you'd be willing to screw over to help yourself, and random people are more likely to help you (even if strangers--you're probably their wife's best friend's greenhouse buddy or something).
2. By removing (or at least reducing) the importance of nationality--assuming a single colony equally represents all peoples of Earth, which it won't--there are a lot fewer conflicting interests to draw resources away from making sure people can survive. A colony won't spend billions of dollars to ferret out terrorists--any terrorists would be turned in by their former friends or their friends, because everyone loses big time if the terrorists succeed, including and probably especially the terrorists themselves. No wars, either, or at least a lot fewer.
Even intercolonial conflicts won't be likely (for a while, at least)--there's nothing worth fighting over and not enough resources to devote to war.