Why the Hegemony of the New Keynesian Model?

The baseline New Keynesian model was not, originally, intended to become a workhorse.

It was intended as a proof-of-concept: to demonstrate that introducing very small market-imperfection frictions into a DSGE framework generated very Keynesian-monetarist conclusions. But the extraordinary shortcuts needed for tractability were and are a straitjacket that makes it extremely hazardous for policy analysis. It cannot fit the time series. And when it does fit the time series, it does so for the wrong reasons.

So why require everything to fit in this Procrustean Box?
This is a serious question–closely related to the question of why models that are microfounded in ways we know to be wrong are preferable in the discourse to models that try to get the aggregate emergent properties right.