The problem is that with most rhinoviruses and most noroviruses, the most common things you're going to run into... The incubation period ( in which you are infected and actively shedding contagions out into the world, but you don't yet realize that you're sick, you don't have the symptoms yet, you're a Trojan horse...) Is anywhere between 12 and 48 hours.
So you think you're okay, or you think your kids are okay, no sore throat, no runny nose, no coughing, no flu, no vomiting, you're "fine"... Until you're not, but you've already spread it all over the place.
And that's the real problem. And that's why washing your hands not just when you're sick but when you're well, and wearing a face mask in public if it's feasible to, are such good ideas. Neither one is 100% guarantee, but it really helps.
Same with getting a flu shot. A flu shot won't protect you against stomach bugs where you're vomiting, won't protect you against the sore throat and stuffy nose of a cold, because those aren't the same virus... The flu shot only works for a specific type of influenza, and you'd be very lucky not to pick up influenza this season (If you do get it, you know) The thing is influenza unlike a norovirus or a rhinovirus has a much higher chance of sending you to the hospital with complications such as pneumonia, and you could actually die. So, we get a flu shot.
It isn't just a protect ourselves, to protect those around us who aren't able to fight off diseases as well as we are.
But that was a good question that you had. Basically, at the very first sign of a cold, if you kept your kids home, and you had to stay home to, or if you stayed off of work, and every single person did this regardless of what their position was, yeah everything basically would shut down! Or we could afford to run a 0% unemployment rate in the country because absolutely every single person would be needed for a job because you need extra people to cover for all the sickies!!
Treasure your health. It doesn't last forever, and it's the most important thing you've got.