So is the rule for starting on 1B solely because the rockets are not guaranteed? Wouldn't this be faster regardless since you wouldn't be required to do 1A?

This is slower, since after 1b with the password you go back to level 1. And in the end you do 1b twice. (I just saw this post, sorry for the late reply).

But yes, the rule was added simply because the drop is not guaranteed, and since you lose about a minute and a half from redoing 1b, I figured it was an acceptable tradeoff.