... Wait, can you not? That's basically how tamiflu works. And one relic of the pandemic will be that at-home covid testing will be cheap, easy and available in a way that at-home flu testing is not (antigen tests are already cheap and easily available in Europe, and soon will be worldwide).
Now, I can imagine that not _all_ cases will be given the antiviral automatically. If you're a vaccinated 18 year old with no comorbidities, say, that is probably not going to be cost-effective (though, well, we'll see what happens with long covid); the chances of you landing in hospital are just very low. But if you're an overweight unvaccinated 60 year old, there's quite a good chance of you turning into a hideously expensive ICU case, and it probably makes sense to provide the treatment.