Isn’t it backwards? If everyone had a little bit of home generated power, then the actual energy part of the bill becomes smaller, and the cost of transmission becomes an even greater fraction of the total cost.
And since transmission cost is typically bundled with the energy cost, it means the final retail energy price has to go up to cover the transmission cost.
With less energy drawn over the wire, the transmission cost goes down since less transmission infrastructure being used. The overall transmission cost should go down as well since there's less need to expand the transmission infrastructure.