"Why dont people just go home when they start to feel unwell"

Because a lot of people either:-
(a) Work for a boss who gets shitty about people taking time off for non-life-threatening illnesses, or
(b) Don't get paid when they're off sick, so they only stay off if they DO have a life-threatening illness (and then sometimes not!), or
(c) Both.

I'm lucky, my employers are very understanding and I get paid. Not everyone's so fortunate.