One common critique of biometric authentication is that if an individual's biometric is compromised, then the individual has no recourse. The concept of revocable biometrics was developed to address this concern. A biometric scheme is revocable if an individual can have their current enrollment in the scheme revoked, so that the compromised biometric template becomes worthless, and the individual can re-enroll with a new template that has similar recognition power. We show that modern deep CNN face matchers inherently allow for a robust revocable biometric scheme. For a given state-of-the-art deep CNN backbone and training set, it is possible to generate an unlimited number of distinct face matcher models that have both (1) equivalent recognition power, and (2) strongly incompatible biometric templates. The equivalent recognition power extends to the point of generating impostor and genuine distributions that have the same shape and placement on the similarity dimension, meaning that the models can share a similarity threshold for a 1-in-10,000 false match rate. The biometric templates from different model instances are so strongly incompatible that the cross-instance similarity score for images of the same person is typically lower than the same-instance similarity score for images of different persons. That is, a stolen biometric template that is revoked is of less value in attempting to match the re-enrolled identity than the average impostor template. We also explore the feasibility of using a Vision Transformer (ViT) backbone-based face matcher in the revocable biometric system proposed in this work and demonstrate that it is less suitable compared to typical ResNet-based deep CNN backbones.