One of the bloods: You’d better bow!
(© Wikipedia)
The Duchess of Cambridge may be the future queen, but for now she’s only the wife of the heir’s heir.
The complexities of the Order of Precedence were plainly laid out for Kate recently when the Queen updated the list of whom should show reverence to whom, and who goes where and when. One wonders if this comes in the wake of Kate’s blunder on the royal barge.
After the Jubilee flotilla on the Thames, the royal barge docked and the royals disembarked. Kate, resplendent in red, started to proceed to dry land, but William stopped her. As he gently guided her backwards, Kate looked slightly embarrassed as Charles and Camilla passed her and went down the steps.
It was a mistake that will unlikely happen again. Whenever the royals are in public, there is strict protocol to follow, nitpicky though it may seem to the average person.
Not only does the OoP dictate who arrives/leaves first, second, and so on, it also states who must pay obeisance to whom. In other words, the Duchess of Cambridge must curtsy to the “blood” princesses – Princesses Beatrice and Eugenie of York, Princess Alexandra of Kent, and Princess Anne. If William is present, however, Kate does not have to curtsy to them.
Where it all started: 
The Order of Precedence has NOTHING to do with who curtsies to whom. It is all about in what particular order a person enters and leaves a venue. As in who is first and who is last. That’s all there is to it! If you see any curtsying or bowing going on between members of the Royal family it is merely a show of respect from one member of the Royal family to another. It has to do with manners and respect and not some law defining who is better or more important than someone else.
It is partly about curtsying, but overall I think it is largely for issues such as order of seating, who leaves when, and before whom. Even though many people find it “antiquated”, I agree with you that it has more to do with respect and manners, so I find it to be a good thing.