This solution only allows for a closed set of states: you cannot extend your system with more states without adding more consts, boilerplate setter functions, and presumably dict entries to map the new states to their methods, or (god forbid) making an if-elif chain longer.
It also makes the case of parameterized states messier, as you will have to dump all the state-specific data into single class, and do something like
wall_direction = LEFT
needlessly leaking data specific to wall-holding to every other state, and increasing the chances of undetected errors (like forgetting to set wall_direction, causing it to use some old value).
If you think of the states in an interfacey record-of-functions sort of way, there is nothing more wrong about the classes instancing each other than there is wrong with 5 - 3 equaling 2 and 2 + 3 equaling 5.