First of all, the government won't go down without a fight. Those teaming mobs won't be squaring of with Elon's plucky group of scientists, but with a military tasked with defending them and motivated by a promise of survival for themselves and their families.
Second, we don't have to worry about protecting acres of land-based solar panels from damage if we're beaming microwaves from orbit. The receiving arrays would be smaller, more defensible, and cheaper to maintain. The powersat could be weaponized to defend its own receiving array.
Third, regarding distance, it's really hard to dig more than a few meters underground without heavy equipment.
Fourth, in a total collapse scenario -- no food, air becomes unbreathable due to methane pollution from melting permafrost --, the people remaining on the surface will die off rapidly. The death squads may last longer, but aren't going to be able to present a significant risk to a deep underground military base protected by the members of the former government with a powersat on overwatch.
After the chaos of the collapse, these locations could quickly begin the effort to repair the atmosphere using all of those terraforming approaches that we would not tolerate being deploying today: ocean iron seeding, orbital shades, bioengineering.
Then the hardened survivors could return to a generally functioning planet, and then maybe go to Mars with their newfound skills.
EDIT: This might seem preposterous, but it's far more viable than shipping one million people to Mars and building up a manufacturing base under time pressure capable of keeping everyone alive and fed while also reproducing a supply chain capable of developing integrated circuits on a world with a different gravitational constant.
This would make sense if Elon's goal was to keep the government alive. It doesn't if his goal is to keep himself and those he cares about alive.
Also most collapses to worry about are not "the Earth just became immediately uninhabitable" but instead "there is a complete collapse in civil order". Think the power grid goes down like it did in 2003, but on a wider scale and doesn't come back up. As we go from inconvenience to mass starvation, what happens?
If you hide away, the survivors aren't just going to conveniently die off. They are going to remain, and WILL have a grudge.
Sure, I would agree if we weren't facing the threat of multiple degrees of warming causing climate changes that will threaten to upend the social order and melt the permafrost within our lifetimes.
If we had room to speculate on the wide variety of disasters that may befall the Earth within the next, say, 200 years, then perhaps hiding underground isn't the optimal best solution.
Aside: I'm sure you'll agree that it'll be easier for Elon to keep his family alive if he's adequately defended. Regardless, he might not have a choice. The third amendment was not always a thing.
My point remains. Disrupted enough to cause the social order to collapse is a lot less disrupted than disrupted enough to cause the environment to be lethal to be in.
As an example of the difference, consider "widespread crop failures followed by food riots causing a general breakdown of transportation networks". The social order is destroyed. But the air is still breathable. And where you live the local crops might even have been fine until pillaged by hungry people.
On a side note, the 3rd amendment has only come up in one legal case, and it was decided in that one that the violation of the 3rd amendment happened, but the government had a qualified immunity because a reasonable person would not have known of the rule. See https://en.wikipedia.org/wiki/Engblom_v._Carey for the bizarre case.
Second, we don't have to worry about protecting acres of land-based solar panels from damage if we're beaming microwaves from orbit. The receiving arrays would be smaller, more defensible, and cheaper to maintain. The powersat could be weaponized to defend its own receiving array.
Third, regarding distance, it's really hard to dig more than a few meters underground without heavy equipment.
Fourth, in a total collapse scenario -- no food, air becomes unbreathable due to methane pollution from melting permafrost --, the people remaining on the surface will die off rapidly. The death squads may last longer, but aren't going to be able to present a significant risk to a deep underground military base protected by the members of the former government with a powersat on overwatch.
After the chaos of the collapse, these locations could quickly begin the effort to repair the atmosphere using all of those terraforming approaches that we would not tolerate being deploying today: ocean iron seeding, orbital shades, bioengineering.
Then the hardened survivors could return to a generally functioning planet, and then maybe go to Mars with their newfound skills.
EDIT: This might seem preposterous, but it's far more viable than shipping one million people to Mars and building up a manufacturing base under time pressure capable of keeping everyone alive and fed while also reproducing a supply chain capable of developing integrated circuits on a world with a different gravitational constant.