Online platforms regularly conduct randomized experiments to understand how changes to the platform causally affect various outcomes of interest. However, experimentation on online platforms has been criticized for having, among other issues, a lack of meaningful oversight and user consent. As platforms give users greater agency, it becomes possible to conduct observational studies in which users self-select into the treatment of interest as an alternative to experiments in which the platform controls whether the user receives treatment or not. In this paper, we conduct four large-scale within-study comparisons on Twitter aimed at assessing the effectiveness of observational studies derived from user self-selection on online platforms. In a within-study comparison, treatment effects from an observational study are assessed based on how effectively they replicate results from a randomized experiment with the same target population. We test the naive difference in group means estimator, exact matching, regression adjustment, and propensity score weighting while controlling for plausible confounding variables. In all cases, all observational estimates perform poorly at recovering the ground-truth estimate from the analogous randomized experiments. Our results suggest that observational studies derived from user self-selection are a poor alternative to randomized experimentation on online platforms. In discussing our results, we present a “Catch-22” that undermines the use of causal inference in these settings: we give users control because we postulate that there is no adequate model for predicting user behavior, but performing observational causal inference successfully requires exactly that.