Interactive fiction uses choice to allow the reader to relate to and bond with the main protagonists in a story better then they would otherwise able to.
An example you use is Huck Finn - a lot of us have read the Adventures of Tom Sawyer in high school but of all those that had there are those that did not gain a lot out of it, or as much as others had. A scene that I was able to relate to in Tom Sawyer was the scene where the boys go into the town dressed as girls and in doing so, they get called out for not reacting as girls are “supposed” to when trying to catch a lead pipe thrown at them. (Or was this in Huck Finn… either way, the point remains) - as the story is written, I was not able to relate to a boy’s adventure as much as I could have if the protagonist was a girl.
The story may change on its face but in its core, it will (if written well) remain the same. The difference is, the author may be able to reach more of her/his audience in a way that creates believable and relate-able connections where none may have existed in a normal fiction …
“Solid characters” is so subjective its not even funny. A solid character is defined by its reception by the author’s audience and a customizeable protagonist is one of the most powerful that can be created. This does not mean the character has to be totally malleable by the reader - Samurai of Hygorai(sp) is a wonderful series of three games which has a popular and somewhat fanatical following and the character has non-customizable traits.
If you ever attempt to write an IF CS game, you will learn, quite fast that a protagonist that is customizable and involves a lot of choices is anything but “whimsical” - I would say it takes much more skill and writing creativity to create a protagonist full of choices then it is to create a normal fiction protagonist.
The story itself is about connecting to and allowing your audience to experience it to the fullest of their ability. If this means it is slightly different every reading, perhaps that is a greater good then trying to fit your entire audience into a structured unyielding story that they may not connect to at times or relate to in critical moments.
One other thing - great character creation really has to do with so much more then identifiers such as gender. I hope you learn that lesson by participating in this community.