To draw supply and demand curves to just find the equilibrium also requires quite a lot of data. And if you aggregate, then it's not even clear what these curves are and what is the equilibrium.
> where the market computes the table for you
I am not sure what you mean by that. How is supply-demand model better? What it gives you in those situations?
Also, I should add: Blatt's IO model (if you want to call it that) is not an econometric (meaning statistical) one. I am not familiar with IO econometric models, so I cannot say how it is different. And it's kinda underdeveloped, too, unfortunately though understandably.
It yields better predictions with fewer inputs. For simple calculations of optimal pricing or optimal production quantities given input costs, a simple table of volume versus price beats a matrix. IO models become interesting when observing entire industries. (That is why the DoJ uses the HH metric [1], an IO-derived metric, to measure competitiveness.) But they're macroeconomic, not microeconomic, models. Macro has a worse track record than micro, which starts with simple regressions of volume and price that we call supply and demand.
These kinds of matrix models are deeply embedded into the IMF's approach, by the way. Many are critical of the IMF's over reliance on such difficult-to-intuit models.
These are commonly called IO models in econometrics (for input-output). There are a number of successful IO models. Characterising these as "competitors" to supply-demand curve drawing is silly since they share common themes and complement each other. IO models need lots of data and underperform in situations where the market computes the table for you, i.e. where prices are clear, e.g. for commodities or liquid financial assets.