Rosenbaum and Rubin’s theorem says that if treatment is unconfounded given covariates X, it is also unconfounded given the single scalar e(X), so units with equal propensity are effectively products of the same coin flip whatever their raw covariates. This collapses the curse of dimensionality that defeats exact stratification.
The workhorse estimator built on it is inverse probability weighting: weight treated units by 1/e(x) and untreated units by 1/(1-e(x)), turning each group into a copy of the full population. Its failure mode is extreme weights where propensities approach 0 or 1, so practice demands an overlap check, a balance audit before and after weighting, and suspicion of any analysis carried by a handful of heavily weighted rows.