Your assumption: > The period where high virus loads are found in our bodies will be shorter is precisely what can't be assumed in advance but must be measure

Your assumption: > The period where high virus loads are found in our bodies will be shorter is precisely what can't be assumed in advance but must be measured, as there are known examples where the assumption doesn't hold at all (and that includes the flu vaccines). (Not to mention that just "shorter" is by definition not "sterilizing", the transmission is then obviously still possible.) If the virus is transmitted via the upper respiratory tract, and it is, it's less probable that the immune cells in blood can prevent the infection and viral shedding of the mucosa. The cells have to be first attacked and infected before the immune reaction can kick in. Even now, it is known that the highest infectiousness of SARS-CoV-2 is often before the symptoms are observable, i.e. before the immune reaction starts. That would also explain the existence of asymptotic carriers: their immune system already protects them, but they are still able to infect others.