There's a lot of problems with industrial ag and monoculture, but I don't think the way that we store and process the grain is really a problem. There's a few different things that a lay person might call a "silo". The taller/skinnier ones are actually silos or grain elevators, which can be used for grain storage. If you see one out on a farm, though, it might be more likely that it's for storing silage. As far as i know, there's no reason you can't have many types of plants mixed into your silage, and having larger quantities in one space makes the fermentation work better.
The shorter/wider silo looking things are "grain bins" for getting grain to the right moisture content. They basically have a screen on the bottom that dry air is pushed through to dry grain and preserve it.
Obviously, we want as much small scale, local agriculture as possible, but part of having a climate resilient system will probably always involve silos.