SC is a bit of a key stage and they are key people on engagements. That is the 'doing' stage rather than the monkey work ot the selling. As such it is useful to you to stay there for while and useful for the firm for you to stay there.
You can spend less time at C. Analyst to C in 2 years is fairly automatic unless you f*** up.
I think grades may have been skipped in exceptional cases but I don't know of any cases personally. Also, promotions occur twice-yearly - the mid-year is not much used but will come in for those on a real fast-track.
Partner in 13 years is not common though! I'll be lucky if I do it in 18, if at all. The next promotion is proving a challenge in itself. You need a particularly favourable combination of circumstances to get to the top quickly.