Should airports and companies be more cautious about allowing sick people on flights?

I took screenshots of a few snippets from different articles. You're free to look at full articles before making a decision.

This is a huge reason why I'm choosing to drive instead of fly on my trip this month. September and October are huge months for illnesses coming about in flight. As a mother to a child who gets sick very easily, I'm not willing to take the chance. I wish people would be more considerate if they know they're sick, but in reality I know they're not and I really don't know how my question could be reinforced. But it's a question that crossed my mind and I wanted to know what others think.