if anything it leaving the game running and letting it play it self proves two things.
1. Valid strategy
2 . The map is indeed a loop with multiple junctions( kirchhoff loop law . The sum of all points is zero.) In other words if you let it run you can go to all points in the map and loop back to zero.
Does this make a rubix cube less fun and less complex to play because you can apply this logic ( algorithm) and eventually solve it.