We analyze the generation rates and preparation fidelities of photon triplet states in pulsed cascaded parametric down-conversion (PDC) under realistic experimental circumstances. As a model system, we assume a monolithically integrated device with negligible interface loss between the two consecutive PDC stages. We model the secondary down-conversion process in terms of a lossy channel and provide a detailed analysis of noise contributions. Taking variable pump powers into account, we estimate the impact of higher-order photon contributions and conversion processes on the achievable coincidence probabilities. At mean photon numbers of ⟨m⟩∼0.25 photons per pulse behind the first PDC stage, we expect around 4.0 genuine photon triplets per hour. Additionally, we discuss fundamental limitations of our model system as well as feasible improvements to the detectable photon triplet rate.