For a typical suburban American home, 80% of the cost is labor and 20% is materials. This rule of thumb even applies in small cases - replacing the floor will likely cost you 5x more to have it done for you vs what the materials cost at Home Depot
Labor inputs make up a portion of a homes cost, so working to automate pieces of the homebuilding process that would lower that cost would lead to decreased prices
But couldn't it just as easily lead to increased profits instead of decreased prices?
Not in a competitive market. Small and medium scale development is usually pretty competitive.