Different units of comparison are used in the market for different property types. Some property types are valued based on the price/SqFt of lot area; some are valued based on price/SqFt of building area; some are valued based on rent multipliers or occupancy ratios; some are valued on the bumber of rooms or the number of units.
Single Family Residences are valued using the sales price itself as the unit of comparison, with refinements for the various differences. There are several reasons for this, not the least of which it is the method used by buyers and sellers in the market. It’s not the only way to do it, but it has proven to be the most accurate and reliable method.
It’s been my experience that the people who rely on price/SqFt/building area for houses are mostly clueless. It’s an almost worthless unit of comparison for houses, except in markets where the data is so similar that there are no differences to account for. Of course, when that happens, the range of sale prices is so narrow that it’s easier just to look at them as a group and rank the subject property within that range.
By the way, you have your value vs. price definitions backwards. Price is what you pay; value is what you get. Once stated, price is a fact, whereas value is an opinion or estimate.