So? They still contracted COVID anyway... Why should I get a vaccine that doesn't work?
A vaccine is forced exposure to a weakened pathogen (rather than natural/environmental exposure to the "real deal"). Regardless of forced or natural exposure, the body's immune system will appropriately respond to the presence of the pathogen (very simplistically speaking, antigens mark cells and viruses for destruction and white blood cells then perform the destruction).
Incorrect... The immune system is continuously working, continuously identifying and destroying cells and viruses. It's not like it just rests on its laurels until infection occurs.
No, it means that vaccinated people still have viruses and cells inside their bodies in need of flagging and destruction. That is not the same thing as infection.
They've just been forcefully exposed to a weakened pathogen rather than naturally exposed to a "full strength" pathogen.
Again, those all sound like your issues, not mine.