"Not Even Once" means that not only did Jonathan Reid refuse to kill save in self-defense but he managed to beat huge numbers of much more powerful vampires without resorting to feeding on others for their power.
Jonathan manages to defeat The Red Queen a.k.a The Morrigan who is the Mother of All Vampires. Admittedly, he was Fighting a Shadow but she was still an avatar that had incredible power.
Jonathan ends the epidemic by defeating her but his scientific knowledge is actually what truly ends the plague as he inoculates himself against the Blood of Hate. This managed to beat King Arthur and William Marshall when they fought it.
It should be noted that while Jonathan is an incredibly powerful bloodline, he's still only a few weeks old at maximum by the end of the game. He's a newborn by their standards and tears through an army of Skals, vampire hunters, and The Dragon of the Ascalon club. Plus, of course, the Red Queen.
The healing of the sick may be busywork for most gamers but in-game, it's Jonathan wandering around London giving away free medicine to people in desperate need of it. The skepticism so many people give you is a sign of just how much of a generous gesture it is.
The fact the staff are staying and working in horrifying conditions to deal with one of the worst plagues of all time. They may be a Ragtag Bunch of Misfits but you'd be wrong to say they aren't all doing an immense service for the public.