Supply is driven by demand unless there is a monopoly in house building (there isn't). If this wasn't the case, one could quickly become a billionaire by starting first company that build small houses that are supposedly in demand but not provided by the market

This is developers maximizing profit per lot.

All this means is there are enough buyers who can afford 2,800 sqft houses to keep builders from wasting a lot on a 1,600 sqft house. There could be a lot more people who want a cheaper 1,600 sqft house (including some of the 2,800 sqft house buyers!) than who want 2,800 sqft houses, but the market will keep delivering the latter as long as the return is better (for the return to improve for 1,600 sqft houses, see about convincing towns and cities to allow smaller lots, smaller setbacks, et c).

You're still presupposing that there's a linear (or at least linear enough to be significant amongst the myriad other factors involved) relationship between square footage of house and cost. And that that relationship extends arbitrarily downwards as you reduce the square footage.