There was more to it: “most of it just went boom”. dilithium destabilized or exploded. A lot of people were killed. This is why I’m confused. It’s not just in short supply, but seemingly dangerous to use. But it’s seemingly used still, despite the potential hazards. And also there might be some other warp capable power source in use.Having to acquire dilithium was also a plot point from time to time on "Voyager", being completely cut off from Federation supply lines. So it has long been established that dilithium is required to matter-antimatter reactions in warp cores, which in turn power the ships and make faster than light travel possible.
It was always a pretty rare and valuable substance; at one point in the second season Stamets stated that one of the reasons the spore drive was developed was to reduce or eliminate the need for dilithium, because of the ecological damage caused by mining for it. It sounds like the Alpha Quadrant's handful of dilithium sources simply ran out of easily extractable material sometime in the middle of the 30th century. Starfleet investigated alternative warp drives that didn't rely on dilithium, but couldn't find any solutions with the utility and reliability of dilithium. Then, at some point, the Burn happened and wiped out the Federation's active fleet.
It looks like the question of what caused the Burn is the mystery that is driving this season.
This always drives me nuts on the Arrowverse DC Comics shows, too. That being said, it made a certain amount of sense here: Mirror Georgiou prioritized the henchmen because they were the ones pointing weapons at her and her comrades. Saru, who didn't approve of any of the killing, didn't have a chance to intervene until the top baddie was the only one left. And by leaving the big baddie's fate up to the people who had been exploited by him, Saru is attempting to establish a reputation for the Federation in this new time period.
The moral and ethical dilemmas faced by Discovery are similar to the moral and ethical dilemmas faced by Voyager during its journey through the Delta Quadrant, in that they're all on their own with minimal to no backup. How far do they bend their code to survive in a time that is no longer easily compatible with their ideals? Or, alternatively, at what point do they choose to accept certain death rather than cross a line that they're not willing to cross?
The bad guy had just murdered one of the locals. He’s oppressed them for years, decades. He deserves death. Sending a guilty man off to hopefully die in the wilderness of parasitic ice is even more retrograde barbaric than honestly judging and executing him.
As story writing it’s sloppy.
As depicting Federation advanced morality, it shows an important lack of understanding of the story itself.
Thats why this hamhanded plotting is so frustrating: it fails in every regard.