Hi OM!
I know you served in the military, which is why I am not understanding why you think military personnel would be so self centered as to jump ship and basically kiss off the world. This runs contrary to my own personal experience and I know a good number of both active and former military personnel. Remember, they were given the choice and also knew that the cure was being worked on aboard the ship. They opted to stay on. Once they decided that and the cure was perfected some did go to seek their families but most stayed on board to help get the cure distributed.
Of course, the lure of the cure would not only keep me on the ship, and I would even fight to protect my presence there. But once the cure was done and I was protected against the disease, I would be off that ship ASAP. Being in the military is a compromise, both on your personal freedoms and on your personal principles. Joining is a voluntary relinquishment of your rights as a citizen (not the vote but everything else). Day in and day out of repetitive tasks, taking orders from others and competing for rank. It is not the life one would choose to live by forever. Even police have at least double the freedom. 90% of military personnel do one tour and that's it (like me). Four years of service? Piece of cake.
Greater good = something greater than themselves, like saving lots of lives.
Okay, but the scientists created the cure and they can distribute it using volunteers on the land. There is no need to protect the ship because the cure now exists and they can dump the ship and start distributing it on land where the survivors are.
As to the notion that people reeling under a pandemic just waving off a restoration of government based on its pre-pandemic behavior, that also sounds a bit off. Just getting the basic government up and running would bring forth more servicemen/servicewomen among other things, and would help get things like basic law and order restored. I would guess that matters like taxes and such won't be high on anyone's docket when as far as we know most of the congress and the bureaucracy are dead. Remember, this is just very basic government not a "restore the whole of the old system" thing.
Basic law and order is an inherent part of primate hierarchy. It would arise on it's own. I am speaking also from a "minority" point of view. The vast majority of people you speak to in America or in foreign nations are not happy with their governments. I do not want to restore something like the government we have today. I would welcome the fall of global military forces, and the collapse of capitalism. I am not alone.