Designating the character you play as for the rest of the game would be a lot like choosing your team in
Maniac Mansion or picking a character class in QFG (and maybe
Unavowed, if I've understood the design correctly): different characters have specific abilities, strengths and weaknesses that open up and close off gameplay possibilities with alternate puzzle solutions and side quests. Maybe one character is strapped for cash, and if you play that character you'll have to look for ways to make money throughout the game, and you probably won't be able to afford tickets to the May Ball and will have to sneak in somehow; maybe one character has an identical twin, and you'll be able to use that to trick people in various ways, but you'll also have to help your twin with their problems; etc. Different characters will have different starting points in various stats (academics, athleticism, social skills, etc.), which you'll need to perform particular tasks and that affect the various in-game rankings, but you'll also be able to influence them by how you allocate your time on different activities.
Similarly, other things you do in the intro might affect where certain clues can be found later on, or other minor details, but wouldn't change the main elements of the mystery or the direction of the story. This is not intended as an emergent or highly branching narrative.
I think different paths, alternative puzzle solutions and multiple/customizable playable characters are necessary to make the RPG/life-sim gameplay elements I have in mind meaningful. The drawback is that it increases the development effort immensely. If I was actually looking to make this idea real I would have to think very seriously about where to cut back and refocus. The great thing about this contest is not having to worry about any of that.