They close the schools to minimize the number of persons each individual comes into contact with, to prevent infection and being infected. Do the math: a typical student has 6 classes of ~25 students per day (many more if you include time in the hallways brushing past other students going to the next class). That means 6 hours of exposure to 150+ other students, in classroom settings, generally close enough to infect / be infected. Maybe they have lunch too, in a room with several hundred other students. A student released from school may sit at home and do homework and only interact with sister Sue and mom and dad, or sit with friends and play Xbox. Or you're right, maybe he/she will go to the mall where they can come into contact with hundreds of others every hour, to say nothing about subway / mass transit rides.

Social distancing works if you minimize your contact with other people, by volume. If there was a significant mortality you know that schools would close, and so might the malls, or at least advisories would read go home and stay home. I am skeptical of whether social distancing will keep you from getting sick - you will get sick if the flu is virulent enough. There's the possibility that your illness might be delayed, and you could find yourself getting sick outside the crunch that exceeds the capacity of the medicos to deal with you.