I was going to mention Rickover but that’s the navy. This discussion has only been about the army. Each branch has their own regs which are probably similar but not necessarily the same. Though I have worked with navy personnel I would not presume to answer questions about their policies. The army does allow general officers to stay on past 60. I think 4 star generals can stay till 70 and probably beyond with waivers.
The First Sergeant is a career field that limits advancement based upon how many people you’re dealing with. A Chief First Sergeant has a much greater number of people to deal with than a Master First Sergeant.
And this bears mentioning, how “First Sergeant” works is different each of the services.
According to http://usmilitary.about.com/od/theservices/a/firstsergeant.htm , and http://en.wikipedia.org/wiki/First_Sergeant , in the USAF and US Marines, First Sergeant represents a specific specialty and once trained for it you can be assigned to be do it at any unit. In the US Army it is the a “command” position at company-level E8, with extra quals on top of the “staff” position of MSG but the person retains their primary MOS, and is assigned to the job at a unit of their own branch (infantry, av, medical, engineer, etc.). Army 1SGs can be selected laterally from among E8s or at the E7-E8 promotion, and (I have observed, at least in Reserves) can move laterally between 1SG and MSG depending on posting; Marine 1SGs are selected at the E7-E8 promotion point and it’s a permanent career track; Air Force 1SGs can be selected laterally or at the promotion point and since 2002 serve for specific, renewable terms with the choice to return to their original field at re-upping.