Frequency-division duplexing (FDD) remains the de facto standard in modern low Earth orbit (LEO) satellite communication (SatCom) systems, such as SpaceX's Starlink, OneWeb, and Amazon's Project Kuiper. While time-division duplexing (TDD) is often regarded as superior in today's terrestrial networks, its viability in future LEO SatCom systems remains unclear. This article details how the long propagation delays and high orbital velocities exhibited by LEO SatCom systems impedes the adoption of TDD, due to challenges involving the frame structure and synchronization. We then present potential approaches to overcome these challenges, which vary in terms of resource efficiency and operational/device complexity and thus would likely be application-specific. We conclude by assessing the performance of these proposed approaches, putting into perspective the tradeoff between complexity and performance gains over FDD. Overall, this article aims to motivate future investigation into the prospects of TDD in LEO SatCom systems and solutions to enable such, with the goal of enhancing future systems and unifying them with terrestrial networks.