Mute city lags on every team combination so badly it's unplayable. Same with FoD. Rainbow ride doesn't and only with specific team combinations it might lag a little bit. I dunno these team combinations, but I presume it has something to do with chars that have projectiles, disjointed hitboxes, double chars or chars that are big. But I've played matches on rainbow ride without any lag or any noticeable lag with peach/falco & fox/sheik teams.
But hey, how about this? If players notice rainbow ride lags in the beginning, the players may call on a stage switch but still follow the cp rules, aka player pick stage, winners change char and losers change char. Neither team/players is also forced to play on RR if they notice a lag in the beginning of the match (the lag should be noticeable with the first movement you can make and not just some parts of the stage).
This should only apply to Rainbow ride as it's completely playable in about 95% of the team combinations and rarely lags compared to FoD and especially mute city, but if it just happens to lag, players may call for a reset. I've never really played on FoD on teams without noticeable lag, neither mute, but I've played many matches on rainbow ride without any noticeable lag. In a dispute about lag one could call on TO to see whether it lags or not, if it doesn't restart the stage and if it does, new stage and possibly chars may be played. I got one tourney where we reset RR cause of stage lag, but my opponents called on it immediately as the game began and we just reset it. It was Peach/Peach and Marth/space animal I think.
But banning RR cause of some lag might be present in 10-5% of the matches and because FoD and Mute are banned for much more prominent lag is not a real reason to ban a stage. You can't just ban this cause this stage might do something similar. Like brinstar has hazard, but it's not in any way comparable to green greens hazard, for example. Stages should be evaluated individually and reasons such as "this and this stage is banned too" should not be the deciding factor in stage banning.