Zero-Knowledge Proofs (ZKP) are protocols which construct cryptographic proofs to demonstrate knowledge of a secret input in a computation without revealing any information about the secret. ZKPs enable novel applications in private and verifiable computing such as anonymized cryptocurrencies and blockchain scaling and have seen adoption in several real-world systems. Prior work has accelerated ZKPs on GPUs by leveraging the inherent parallelism in core computation kernels like Multi-Scalar Multiplication (MSM). However, we find that a systematic characterization of execution bottlenecks in ZKPs, as well as their scalability on modern GPU architectures, is missing in the literature. This paper presents ZKProphet, a comprehensive performance study of Zero-Knowledge Proofs on GPUs. Following massive speedups of MSM, we find that ZKPs are bottlenecked by kernels like Number-Theoretic Transform (NTT), as they account for up to 90% of the proof generation latency on GPUs when paired with optimized MSM implementations. Available NTT implementations under-utilize GPU compute resources and often do not employ architectural features like asynchronous compute and memory operations. We observe that the arithmetic operations underlying ZKPs execute exclusively on the GPU's 32-bit integer pipeline and exhibit limited instruction-level parallelism due to data dependencies. Their performance is thus limited by the available integer compute units. While one way to scale the performance of ZKPs is adding more compute units, we discuss how runtime parameter tuning for optimizations like precomputed inputs and alternative data representations can extract additional speedup. With this work, we provide the ZKP community a roadmap to scale performance on GPUs and construct definitive GPU-accelerated ZKPs for their application requirements and available hardware resources.