I think it's too much to say that stage hazards can decide the outcome of the game, but more like they can influence the outcome of the game. The thing about stage hazards is that everyone know exactly what they are ahead of time, so there isn't any luck involved--this is unlike items, which appear out of thin air semi-randomly.
It may be hard to make a great case about items, but stage hazards/bosses are predetermined, and I think there isn't a great case for banning stages based on them. The only reason I see there being a need to banning a stage is when the stage changes platform/etc positioning to where the players just stand around for a long time until conditions change again, or where certain areas of the stage are dangerous enough both to approach and to leave and no one will move (camping). But many other stages have hazards and/or transform where this is not the case.
Everyone knows what stage hazards exit before the match begins. Wind direction and speed on gameday can influence a match, but both teams know what is happening at the exact same time. Depending on which team has the ball going in which direction, it may be unfortunate, but it's not unfair. It's just an element of the game that has to be taken into consideration. 90% of the time it doesn't determine the match, the better team almost always wins. Same goes for golf--players aren't allowed to say they won't play until wind conditions are exactly the way they want them to be, or exactly the same as when another opponent will be/was playing. Most outdoor team sports play in most weather conditions. It just lead me to the position that Smash players banning certain stages are akin being poor competitors because stage conditions affect how you play.