It's a matter of balance. If you want to avoid making people around you sick the best way is to avoid exposing them when you are ill. People going in to work when ill is the classic example of that - and the circumstances that force some people to feel that they need to do that are problems in both the workplace and the society. But constantly generating pollution on the off chance that you might have something that is asymptomatic but might infect and affect someone else is a lack of proportion (it's different in a medical environment, with vulnerable people and likely more pathogens in the environment, as the balance of risk and harm differs). And you were advocating this as something that should be done generally, not just as a personal thing, which is what would make it problematic. Weighing one type of benefit against a different type of harm is tricky, but I'm afraid that I feel (very strongly, as you can probably tell) that you are are attaching too much weight to one and too little to the other.
As for trusting your city's waste disposal system, I'm saying that trust should not be blind - and neither should mistrust be automatic (which is another source of problems). If there are problems the solution would not be to incinerate stuff yourself (which you don't have the capability of doing properly), but to get those problems fixed (which one individual cannot do, but collective action can). But the big point is that no matter how good their systems are they are still much worse than not generating the pollution in the first place, and hence even if their systems are world class that doesn't remove the need to reduce rather than increase the waste we generate.