For most real time systems, including many games, it doesn't matter if one is more efficient than another because what matters is the predictability that comes from always rendering a complete frame in 1/60th of a second.

In many cases checking if absolutely nothing changed in a system isn't trivial either. You either have very fine grained tracking which involves a great deal of complexity and increased memory cost, or very broad tracking which results in a lot of false positives.

No, if it takes 1 ms to check if things have moved, and 5 ms to do the pathfinding then the worst case is 6ms when something moves. A guarantied 5 makes for a more stable frame rate than a sometimes 1ms, sometimes 6ms calculation. Often times 60 FPS average with high variability feels worse than 30 FPS with low variability.