Because you have to remember that coronavirus is just something added to all the different diseases that existed 6 months ago.
There are tons of bacteria, virus, fungi whose infection could resemble COVID-19 sindrome (i remind you that symptoms can vary and the same symptom can present differently in different patients) that can be treated with simple antibiotics therefore avoiding strict quarantine for that person (and all the related family)
tests are not perfect you are right they are only truthful 90%,95%,99% of times therfore giving a pretty precise estimation of whats happening in the population and all related statistics (on which all the prevention is based, the government decisions ecc...)
Obviously the test is just a "screenshot" of what's happening in a certain person in a specific time and the optimal situation would be take the test every day for every person butsince that is not feasable 1 test every few weeks (or at least one) is good enough still leaving test kits available for people that need a more precise evaluation of the sistuation (people infected, in hospitals, in retirement homes...)
p.s. the so called "personal perspective" in a pandemic is not worth considering since a lot of the decisions taken from my personal perspective do not make any sense but are extremely important from the community perspective (example: "why on hell shouldn't I go outside if there is nobody out there to get the virus from?" makes sense for me as a single but it's deleterious from the society perspective)