Geometrically nonlinear structural problems are commonly analysed using formulations that differ in how nonlinear kinematics are represented and treated at the equation level. Alongside approaches that retain the governing relations in an explicit nonlinear form, including trigonometric dependencies, various geometrically exact finite element formulations employ incremental or corotational treatments of large rotations. While these approaches often produce comparable equilibrium solutions in standard benchmark problems, their numerical convergence behaviour is less clearly understood. In this contribution, we examine the convergence behaviour of selected geometrically nonlinear beam formulations, focusing on materially linear problems involving large rotations, such as cantilever bending and elastica-type responses. Within an explicitly nonlinear kinematic framework, different discretization strategies are considered, including both primal and mixed-type formulations, allowing the influence of discretization choices to be examined alongside the representation of geometric nonlinearity. In addition, alternative formulations employing implicit and geometry-based representations of curvature and rotation are included as comparative references. Differences in convergence behaviour are observed between the considered formulations. Effects commonly associated with locking phenomena may manifest in distinct ways depending on the formulation, influencing both convergence behaviour and apparent stiffness. The study aims to contribute to a clearer conceptual and numerical understanding of these effects in large-deformation beam analysis.