"expected to be the same" is simply not true.
Even simple models like the one described at https://youtu.be/k6nLfCbAzgo?t=920 (I point to the relevant part) shows that reducing the infection rate can also lead to fewer overall deaths.
Even simple models like the one described at https://youtu.be/k6nLfCbAzgo?t=920 (I point to the relevant part) shows that reducing the infection rate can also lead to fewer overall deaths.