It helps you know how strict you need to be within your household to prevent members of your household from becoming infected. It's difficult to sustain the level of vigilance needed to protect someone living with you in the next room if you're having extremely mild symptoms and you're not sure you're positive. If you know you're positive you could do something like get a hotel room for 2 weeks to protect your family.

Right. You can walk out of the testing facility and get infected on the way home.

Too many people have said "I was tested, I don't have it", completely treating it as a continuum, not a point in time.

There's a difference between the kind of quarantine expected with a positive test vs not knowing. Once you test positive, you're not supposed to leave the house at all for 14 days, and only then with clearance from the local health department (or physician depending where you are). If you don't know for sure that you had COVID, it would be reasonable to go back out after your "cold" symptoms alleviated.

Part of the trouble is that there seems to be a lot of variation in symptoms in people who test positive.