Yes, of course power sinks gain value from having their own power buffer, even if only to take advantage of fluctuations in energy cost. But why would this cause grid collapse? They still need the energy delivered, at some point. It puts whoever runs the grid in the quite enviable position of power market middleman. Far from collapsing, I would expect grids to do extremely well out of such a shift.
An apartment depending of where it is may put in batteries if it is in a location where power sagging/failures happen often.
Remember the entire world is not North America or Europe.