Your predicate is wrong and your conclusion is therefore wrong (and doesn't follow from the predicate anyway).
In other words, you're talking rubbish.
People who are ill don't get the same quantity and quality of work done. Illness also makes a workplace more unpleasant, which has some adverse effect on work, but that's harder to quantify.
Say, for example, someone comes into work with a highly infectious disease. It's not a particularly bad disease (e.g. a cold), but it reduces their effectiveness. In some jobs it would reduce it quite a bit, in other jobs less so. They'll be a bit slower physically and a bit slower mentally and a bit distracted by the sneezing and the mucous dripping out of their nose and the discomfort. It's far from crippling, but it has some effect. They'll have to spend some time dealing with the symptoms - not much time in any one go, but little bits of time quite frequently. Overall, in terms of quantity and quality of work, maybe they're at about 80% of normal.
So if they come in, their employer gets 80% of normal work for their wages. Which is obviously better for the employer than paying them in full to stay home and therefore getting no work for their wages...but while at work they infect 2 other people, who in turn infect 5 other people and now the employer has 8 people working at 80%, a loss of 160% of the work of one person, i.e. more of a loss than the original 1 person staying at home on full sick pay.
In short, it's not obvious and clear-cut which course of action is a smaller cost to the employer.
I'd say that a cold is probably not enough illness to justify time off sick, but I wouldn't completely rule out the possibility that it might be a lesser cost for the employer and it's better for other employees.