Low Earth Orbit (LEO) satellite communications (SATCOM) offers high-throughput, low-latency global connectivity to a very large number of users. To accommodate this demand with limited hardware resources, beam hopping (BH) has emerged as a prominent approach in LEO SATCOM. However, its time-domain switching mechanism confines coverage to a small fraction of the service area during each time slot, exacerbating uplink throughput bottlenecks and latency issues as the user density increases. Meanwhile, wideband systems experience the beam-squint effect, where analog beamforming (BF) directions vary with subcarrier frequencies, potentially causing misalignment at certain frequencies, thereby hindering the performance of wideband SATCOM. In this paper, we aim to shift the paradigm in wideband LEO SATCOM from beam-squint as an impairment to beam-squint as an asset. Specifically, we put forth 3D rainbow BF employing a joint phase-time array (JPTA) antenna with true time delay (TTD) to intentionally widen the beam-squint angle, steering frequency-dependent beams toward distributed directions. This novel approach enables the satellite to serve its entire coverage area in a single time slot. By doing so, the satellite simultaneously receives uplink signals from a massive number of users, significantly boosting throughput and reducing latency. To realize 3D rainbow BF, we formulate a JPTA beamformer optimization problem and address the non-convex nature of the optimization problem through a novel joint alternating and decomposition-based optimization framework. Through numerical evaluations incorporating realistic 3D LEO SATCOM geometry, our numerical results demonstrate that the proposed rainbow BF-empowered LEO SATCOM achieves up to 2.8-fold increase in uplink throughput compared to conventional BH systems. These results mark a significant breakthrough for 6G wideband LEO SATCOM.