Putting my nose where it doesn’t belong and not to drag out the discussion, but the reason that it is not allowed is primarily a timing issue. Self-seeded swim starts are different and you can line up wherever you want with whomever you want in those because you go into the water in very small groups and the timing mat is at the very end of the dock/pier as you go into the water.
Wave starts for triathlon are done differently. For these, the race organizers put people into age groups or sets of age groups in the computer and assign these people to a wave. When the start gun goes off, they push a button and record a start time for that wave. Everyone in that wave is then automatically assigned that gun time. You do not cross a mat in wave starts to start your timing chip (running races are different in that you do so your chip starts when you cross that mat and not when the wave starts, but you cannot do this in the water). If you ever cross a timing mat at a wave start triathlon before going into the water, this is for one purpose only: to see who has gone into the water so that they can compare that list to who comes out of the water.
But if you were to jump to a different wave, then your race clock becomes incorrect because you were assigned to a specific wave which was given a specific start time. While jumping back technically just adds time to your race clock, what’s to stop someone from jumping ahead and cutting off time from their swim. So while yes, it’s easy to change one person’s start time if they jumped waves it becomes a timing nightmare (almost virtually impossible) if you just let everyone do that as they want to. So the best thing is just to flat out say: no, it is not allowed.
It actually can become a serious safety issue too because the race organizers expect a racer to go in the water at a certain time and should something untoward happen, then when they start sending out the emergency response teams, they could be asking the wrong people (“hey, this person was in your wave, when did you last see them?”) in their efforts to find a lost participant. And that could waste a lot of the responders’ time trying to get rough whereabouts and risk a person’s life in the process.
President | DC Triathlon Club