In some other countries, rapid home tests for flu, RSV, and COVID-19 are available:
These combination tests are available in Europe for 6.5 €. A combination test is available in the US, but requires mailing the sample to a lab, and costs $169.
Strep testing is usually done with a swab of the throat (rather than nostril), so it would not combine well with flu, RSV, and COVID-19 testing. It would also be more difficult to self-administer even if it were available as such.