Having a strong, well-integrated core is important not just for proper alignment in yoga postures, it is a key component in keeping good alignment in every walling application
The core is the support system for the middle mid section. It creates a reinforcing framework to counteract the pull of gravity and keep the everything balanced and integrated, even if and when things start to move around. Having a strong and balanced core is a key to preventing collapses and back problems. Think of the core as the structural foundation that supports everything, just like the structural frame that upholds a building. The stronger the core, the more stable the thing is.