The concept of center of mass is a concept invented by US.
Considering the porous nature of matter, most of the time there
may be nothing at that point. Investing a device with a reality it
does not possess and saying F(t) = ma(t) is symmetric with
respect to that does not make sense. We have to remember that
sooner or later we have to translate the results we obtain in terms
of center of mass into motion of objects in the real world. Otherwise
they will not be of any use.