Quadruped animals seamlessly transition between gaits as they change locomotion speeds. While the most widely accepted explanation for gait transitions is energy efficiency, there is no clear consensus on the determining factor, nor on the potential effects from terrain properties. In this article, we propose that viability, i.e. the avoidance of falls, represents an important criterion for gait transitions. We investigate the emergence of gait transitions through the interaction between supraspinal drive (brain), the central pattern generator in the spinal cord, the body, and exteroceptive sensing by leveraging deep reinforcement learning and robotics tools. Consistent with quadruped animal data, we show that the walk-trot gait transition for quadruped robots on flat terrain improves both viability and energy efficiency. Furthermore, we investigate the effects of discrete terrain (i.e. crossing successive gaps) on imposing gait transitions, and find the emergence of trot-pronk transitions to avoid non-viable states. Compared with other potential criteria such as peak forces and energy efficiency, viability is the only improved factor after gait transitions on both flat and discrete gap terrains, suggesting that viability could be a primary and universal objective of gait transitions, while other criteria are secondary objectives and/or a consequence of viability. Moreover, we deploy our learned controller in sim-to-real hardware experiments and demonstrate state-of-the-art quadruped agility in challenging scenarios, where the Unitree A1 quadruped autonomously transitions gaits between trot and pronk to cross consecutive gaps of up to 30 cm (83.3 % of the body-length) at over 1.3 m/s.