This is hard stuff. It's probably because it's Ni lead, which means it's out of our tangible, explicit understanding. Hopefully writing ideas back and forth with a few of us will help.
I too have big dreams, also in many areas. And am young enough, have a baseline of talent in enough areas, that they're all reasonably feasible (assuming I work really hard once I commit).
If I'm incompetent at something I try hard at, I feel so small. When I am really competent, especially where others are not, I feel almost whole. It's purpose-driven, I suppose.
Maybe it's because Notably Excellent Human Beings are all superbly competent at what they've committed to. (Even human rights things: Ghandi, Mandela, MLK, etc... they all had to be competent enough to succeed, build a following, corral the followers, improve, etc.)
I think it's legitimately well-intentioned, for the good of all, that I feel the need to be competent. Sure, it manifests itself in selfish ways, often. But I think that's the pale reflection of the true drive.
But why am I driven so hard? I don't know.
Maybe it's because I'm female, but I'm also superbly driven to be an excellent wife, mother, and friend when the time calls for it in my life. (Friend, I suppose, being now.) Relationships--I need to be competent there, too. I think that's why I'm so driven to learn MBTI: I want to pwn them. I want to get inside people's heads, I want people to spill their souls to me because they know I'm trustworthy and can hopefully help them reshape their insides more sturdily...
I am also extremely aware of how little time I have to accomplish all of this. My time is my most hoarded possession. I want to figure stuff out and then go use it in my relationships, in my career where I'll make a serious difference in people's lives...
I don't know what drives it but I also don't know if I can articulate to any non-INTJ just how strong this drive is.