If each choice matters then any good writer will give you a blank protagonist because they need to account for whatever the user chooses, otherwise in many choices he would be acting out of character. Down each path they can get more detailed with his personality because there are less options, however, when he is first introduced he is a blank slate.
Every character looks like a blank slate for the player when the game start, because he know nothing about him/her. What doesn't mean that they don't already have an effective personality, that will be shown all along the game. As for the choices, they don't fill the blank, they reveal a part of the personality ; they can also change a part of this personality, because human's personality isn't something frozen, it evolve depending of the circumstances.
It's how a game works, how the personality is handled ; a journey during which you will, more or less slowly, discover the characters you interact with, through the decisions you'll make.
It doesn't have to be like that, you could write a very detailed protagonist with a sharply defined personality, but you'd have a terrible story, as he will often be acting out of character, the mark of a terrible writer.
I'll go further than you. It's not that it doesn't have to be like that, but that it have absolutely no reason to be like that if you're effectively a good writer.
As author, you are the one who present the choices, therefore you already know how to handle them in order for the character to stay true to his/her personality. You haven't just thrown some choices, you have thought about them, weighted the effect that each one will have on what's coming next, and prepared yourself, and your code, to handle them.
There's absolutely no difficulty to handle this, both as writer and as game maker. All you need is to have planed it when you decided to offer this choice to the player.
Therefore, few variables at the right place, few tests at the right moment, and you'll have a scene that will look totally different, depending both of the choice made by the player, and of the personality of the other character(s) involved in the scene.
If the writer is good and chooses this type of protagonist, he would only give you superficial choices that only decide which girl you end up with and whether it is a good or bad ending, but the lion's share of the game would be essentially linear, each path having the same core story but with different dialogue.
You can doubt what I said if you want, I really don't care, but you can't imply that it's impossible to make games that will have both, characters with a strong and deep personality, a good and consistent story, while relying (more or less) intensively on choice, and this without the characters being a single second out place. And there's a really good reason preventing you to make such implication : such games exist.
I gave you an example, few others gave you more. If those games exist, and they exist, then you are wrong, dot.
To put it in a hard measure, I would say it is 40% story, 60% scenes. For me.
