In this paper, we question the accuracies and validity ranges of conventional geometry-based one-ring models (GBORMs) and their variants whose correlation functions (CFs) are based on approximate total propagation distances (TPDs) under a small beamwidth (or small angular spread) assumption. To answer this, we use a reference GBORM for space-time-frequency (STF) correlated channels and analyze the accuracies and validity ranges of the conventional models. Our analysis shows that the conventional models become inaccurate for urban pico/micro/macrocells, vehicular-to-vehicular, and wideband channels, where large beamwidths and relative propagation delays are typical. In order to remedy these issues, we propose new TPDs and closed-form STF-CF using novel approximation methods with Jacobi-Anger expansion and show their superior accuracies and validity range. The new closed-form STF-CF represents or includes conventional closed-form CFs as special cases for small beamwidth. Also, it has favorable properties facilitating its use in a wide range of propagation channels. The applicability of the new solutions to conventional wideband models are tested and verified based on measured data.