Infantry;
I feel like some formations should be static only i.e. square and circle and once asked to move go back into default or line formation, i dont think its viable to even move in some formations or realistic.
The fastest formation should be line/loose formation, makes more sense as it takes less coordination to just stand in a line etc...
I would like to see Skein used for inf more and changed a bit, i feel like skein should be used to break a shield wall and punch a hole, so maybe a short burst of speed once applied as to charge.
Cav;
Agree with shield formation, there really isnt any need for this to affect speed, remove it or make it same as line formation.
Realistically using shield formation to cheese the ai into pulling out a spear should be patched, only real reason its used for atm is protecting rider while a ramboing cav captain is dealing with enemy cav, maybe combining the speed boost in skein you are talking about and shield formation for a "break charge" to knock over or punch a hole in a shield wall might be the best way to go.
Archers;
I mean the formations are broken completley, ive had my own ai archer firing into the back of anothers head in square/circle formation, i think you should have special formations for archers, a split group formation would be good