I would agree with your evaluation and propose an even more accurate prediction would include the aspect that a 50 gallon water heater or a dishwasher costs the same regardless of 1500 sqft or 6000 sqft so the ideal formula is probably some linear equation with a fixed amount plus a sqft amount. $1500 plus $1/sqft per year maybe a good start.

Except the 6000 sqft house has 2 water heaters, 2 or possibly 3 hvac systems and another bathroom or 3.