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Problem definition: Contrary to classic applications of matching theory, in most contemporary on-demand service platforms, matches can not be enforced because workers are flexible – they choose their tasks. Such flexibility makes it difficult to manage workers while keeping customers satisfied. We build a framework to compare platform matching policies with less flexible and more flexible workers, and empirically quantify by how much worker flexibility hurts customer satisfaction and customer equity. Academic/Practical relevance: In academic literature, there is no established framework that allows for the comparison of matching policies in on-demand platforms. Further, the link between worker flexibility and customer satisfaction is understudied. Methodology: We propose a tripartite framework for empirical evaluation and comparison of the operational policies with different degrees of worker flexibility. Step 1: Predictive modeling of customer satisfaction based on estimation of individual unobservable characteristics: customer difficulty and worker ability (item-response theory model). Step 2: Evaluation of the effect of matching policy (under a given level of flexibility) on customer satisfaction (bipartite matching). Step 3: Quantification of the associated monetary impact (customer lifetime value model). Results: We apply our framework to the dataset of one of the world's largest on-demand platforms for residential cleanings. We find that customer difficulty and cleaner ability are good predictors of customer satisfaction. Granting full flexibility to workers reduces customer satisfaction by 3% and customer lifetime revenue by 0.2%. We propose a family of matching policies that provide sufficient flexibility to workers, while alleviating 75% of the detrimental effect of worker flexibility on customer satisfaction. Managerial implications: Our results suggest that, in platforms with flexible workforce, the presence of worker and customer heterogeneity reduces customer satisfaction through matching inefficiency. Our empirical framework helps practitioners to decide on the right level of worker flexibility and the means for achieving it.