As far as I can tell, if you have Frontal and Right Profile the puppet will not switch from frontal to the profile when you use the arrow key. You have to create Left Profile as well for the flipping from “Frontal” to “Right Profile”. If the right profile is the default (like walkbot), then walking works. So it is not the walk behavior that seems to be the problem, but rather the code to decide to flip from the default profile to the walk direction profile refuses to work without Left and Right profiles both defined (and rigged sensibly).
I think it makes sense to allow Frontal with only one profile. Puppets can walk backwards if the other profile is not defined - and this works pretty well! So allow only one of the two profiles to be defined, allow it to flip from frontal to the side profile, then make it walk forwards/backwards based on which arrow key was pressed.