The ability to enforce robust and dynamic access controls on cloud-hosted data while simultaneously ensuring confidentiality with respect to the cloud itself is a clear goal for many users and organizations. To this end, there has been much cryptographic research proposing the use of (hierarchical) identity-based encryption, attribute-based encryption, predicate encryption, functional encryption, and related technologies to perform robust and private access control on untrusted cloud providers. However, the vast majority of this work studies static models in which the access control policies being enforced do not change over time. This is contrary to the needs of most practical applications, which leverage dynamic data and/or policies. In this paper, we show that the cryptographic enforcement of dynamic access controls on untrusted platforms incurs computational costs that are likely prohibitive in practice. Specifically, we develop lightweight constructions for enforcing role-based access controls (i.e., $\mathsf{RBAC}_0$) over cloud-hosted files using identity-based and traditional public-key cryptography. This is done under a threat model as close as possible to the one assumed in the cryptographic literature. We prove the correctness of these constructions, and leverage real-world $\mathsf{RBAC}$ datasets and recent techniques developed by the access control community to experimentally analyze, via simulation, their associated computational costs. This analysis shows that supporting revocation, file updates, and other state change functionality is likely to incur prohibitive overheads in even minimally-dynamic, realistic scenarios. We identify a number of bottlenecks in such systems, and fruitful areas for future work that will lead to more natural and efficient constructions for the cryptographic enforcement of dynamic access controls.