I doubt what you have in mind for the story is woman in the world bangs the MC or doesn't get the cure, It's just where the story is at now makes it funny to think about. As it stands 100% of the people who have gotten the cure have gotten pregnant and have all gotten cured the "old fashion way".
Most of it was just saying it's a weird situation to be in You literally hold the fate of all humanity in in your pants. Dynasties that don't join with you for the night wouldn't pass the current generation.
In rulers past sex was often tied with rule you would dilute the bloodline like the Khan did, or with the practice of Prima Nocta. This though isn't like that no barbaric rule rendering that under Caesar which is Caesar's, it's ensuring that a dwindling population can survive. The world is your harem to save humanity from the Prophet's choice to infect it. (thought the current religious leader was called the prophet, like some cults have it, but my mistake).
The khan bit was about how 1% of the total world population is related because of how he ruled. If the MC has to sleep with everyone once, and people in general have between 1 and 4 children, he's going to be directly related to about 33% the first generation give or take and about 75-80% of the next. It's an even weird situation if you think it that way.
There's also some negatives with that route you couldn't have a polyamorous relationship as you can only really be with a woman once. It would limit the ability to cure people if you did and the MC's kinda on that path. If you don't sleep with enough people also there's the problems of an endangered species where the genetic pool is to small to be sustainable. Do you do the ugly chick or do you not take the risk of impotence and being unable to save enough of humanity it can save it's self. If you don't do her and she's tied to a dynasty that will rebel and kill enough people you can't save the population would that change your choice?
Anyways just strange to think about how that would play out in an actual senecio where the world was depended on one mans baby batter to procreate a plentiful future. While it would make for a hilarious Powerpoint from legacy if he nails some of the details of the "ins and outs" of the problems with delivering a cure at scale that way.. like I started with I don't think it's really the direction you are taking, but it's funny to muse. I get legacy has hinted at making it contagious so it self propagates. It's just boring to think of the cure like covid or the pox.