I hate the fact that the typical mechanism for the side step in fighting games is the double tap. Effective stepping to the side requires timing and speed and a double tap especially with analog sticks makes the side step take longer to pull off, meaning that you basically have to time and initiate the step before a punch is thrown which promotes doing it randomly and hope for the best or you have to slow other parts of the game to make it more effective.
I think that the side step should be context sensitive, where when im in punching range a quick tap of the stick that will break the recentering mechanism if your opponent is in a punching animation. Also I should be able to perform a check hook or other punch if i initiate a side step and a punch at the same time. The range of side stepping should be widen in the cases where the opponent lunges at you with shots.
Also, recentering should only be automatic when a player is performing no other action other than movement. Meaning a person holding parrying or weaving stance can't auto center, nor should a parry or weaving be as functional against a person has moved off to the side. This would force people from constantly holding those stances and actions.
Also the side step action could be used when breaking a clinch (which should be allowed more liberal use) to move off to the side and not straight back. If you engage in a clinch because you on the rope, the last thing you want to do is break the clinch and land right back on the ropes.