I did not imply you were stupid, Water Bob, just that you like a word people around here find stupid more often than not. I read and posted in many of your recent threads (starting with "Stealing the Nish", btw), and even though I rarely agreed with your view of rules interpretation etc., the discussion was always fruitful in the end, in that it gave everybody something interesting to talk about. In this case, I was really only making a tongue-in-cheek observation.
And in order to contribute something useful to this thread's topic, as well: In Hârnmaster, which I used to play a lot, Initiative is a skill which everyone opens at start of play, at a rather measly value. Warrior types get better starting values, and others can use option points to increase it if they wish. Later on, the skill is raised just like any other skill, i.e. by training and using it while in tough spots.
In Hârnmaster, Initiative rolls can succeed or fail. Failing it means you lose a whole turn, since you cannot muster enough 'initiative' to attack - the skill is thus a measure of your ability to leap into action without second thoughts, and is in good part based on Willpower. Veterans have a much easier time committing themselves to a furious mêlée, in that they have much better initiative, but even they may falter on occasion, not daring to join the fray, merely defending themselves for the time being.
I always found this handling of initiative appealing: this way, it's not about being quick, it's about the psychology of combat. It combines a morale factor with hard-earned battle experience and an instinct for violence.
Your idea of adding BAB onto Initiative seems to work a similar angle, and I like it.