“Should I level up my stamina, knowing that I’ve got the “sick” status modifier from here on out? Should I spend time side questing when that inevitably means I have to spend more time staring at this dying man’s face? Morgan talks constantly about how things are coming to the end. What’s my motivation to do anything but just getting on with it?”
Levelling up is still levelling up, so, yes. Looking at his face puts you off doing side quests? What kind of logic is that? Not to mention the sickness is a big wake-up call for Arthur and he tries to better himself because he is running out of time, something you see when doing the side quests.