A bit late with this one, but I feel that this has to do with Kojima literally not mapping out the full extent of her character. Basically, Kojima has gone on record to say that a lot of her character wasn't really planned, and sort of just developed naturally as production in the game (MGS3) went on.
I will disagree with the early notions that Big Boss feels like a mishmash of Snake and Raiden. Snake always came across to me as the classic Hollywood anti-hero, complete with one-liners and the constant womanizing (MGS1 and MGS4 made this very obvious). He also tends to philosophize more than the other two and while he's no science geek, he's still well-acquainted with worldly matters. Raiden may have been a bit derpy, but he was savvy with general world knowledge and even in MGR this is pretty evident (which fit with Rose's character concept as a "normal" woman to complement Raiden). I always thought that Raiden's naivety came from the mindscrew that was Big Shell and the S3 plan. Big Boss on the other hand always felt like a super naive than the other two, and his expertise mostly lied in military-oriented topics such as guns or sociopolitical events relating to warfare and revolutions. The guy barely showed any decent worldly knowledge outside of military topics, tended to be more sympathetic towards his enemies (less talky or snarky too), and he's actually the least savvy in terms of normalized social interactions compared to Raiden and Snake.
Honestly the whole "Jack" thing is pure coincidence. Raiden and Rose were given their respective names as a romantic homage to Titanic's Rose and Jack. In Big Boss's case, John is his real name (so the whole John Doe thing is sort of meant to be ironic), and Kojima has gone on record to say that "Jack" was just his personal nickname that was used by The Boss. Considering that Big Boss' personality traits seems very Japanese-inspired in its execution and humor, this isn't much of a surprise as using personalized nicknames are fairly common in Japanese works, often as a significant way of showing how close the characters are (The Boss and Big Boss in this case). I think one of the main issues with Big Boss's personality is that by allocating this sort of anime-esque naive would-be hero personality (unlike Snake's more snarky/gung-ho action hero type or Raiden's worldly savviness and self-indulgence), it's a little harder to transition the character from hero to full-on bad guy.
Still, for all the complaints leveled towards PW here (seriously, the game presented some interesting stuff for BB and I felt it wasn't all just fun and games), I honestly thought it provided the best transitional phase Big Boss since it showed his militaristic side and how much of a realist he is compared to Snake's more liberal mentality. Just look at Snake's final speech in MGS2 a lot of it tends to contradict BB's more conflict-oriented mentality.