Why the marketed rapid tests of COVID-19 aim to detect the antibodies produced in infected patients and not the antigen directly. is it difficult to detect it directly?
Maybe because the rapid tests that detect the antigen directly have many limitations or are dangerous because you need to handle the viral antigen directly!!! they are also limited by the Sensitivity that depends on the patient's viral load...In general, the rapid lateral flow immunoassays that are most available on the market of several medical conditions (not only for COVID-19) are designed to identify antiviral antibodies.
However, there are some tentative, for COVID-19, even they are very few... you can find in this link all types of selected diagnostic tests available until now.