Muscles have a certain capacity to perform work. The larger the capacity, the more reserve they have. A strong muscle is less likely to get injured to comparison to a weak muscle.
Your squat muscles include quads, hamstrings, glutes, core etc – is your squat muscles can sustain and lift a heavier one-rep-max, your body will certainly be more resilient to injuries.
Standing up and sitting down would be an easier task. Navigating stairs or going on long walks/hikes wouldn’t be such an issue with strong legs and core.