That's the desired outcome of competition but the effects can go all over the place and the second-order effects in fragile towns can matter more than the price drop. As an extreme example, some people may lose their jobs, local spending may fall, some small shops may close and Aldi may pull out too, so everybody loses (here's [0] as an approximate example).
Usually a community can tolerate changes only when it's not already near the bottom. When you're near the bottom, almost any destabilisation can kill your little system.
