The "Save" stat was watered down, I think, around 1969.
Some things about baseball are still evolving - a sea change (equivalent to the extinction of the dinosaurs) was Tony La Russa developing the late-inning specialist-centered bullpen.
The 'pen used to be just five guys who couldn't throw 300 solid innings a year. Look at the now-seemingly ridiculous workloads pitchers had to toil under pre-1968. Think of how much longer careers could have been extended (e.g. a Mel Stottlemyre or Warren Spahn). Everyone has a "closer" these days. Most if it, I think, is because of the large guaranteed contracts given to players: creates economic incentive to avoid excessive wear-n-tear, and that shows up on the field.
maybe but you have to have stones to be a closer for 10-15 years, and a rubber arm that can throw 2 or 3 innings (counting warm ups, bullpen tosses and in-between innings) every other night.
Some guys are just fit to be a closer. Rivera is one of them. Others are not (Brad Lidge??).
Just watch, the save will be the next big stat. Right now, for pitchers, it's 300 wins or 3000 strikeouts, but now it's going to be 300 or 350 saves.
If you look at how starting pitching is going and who is doing the best, we MIGHT have the last couple 300 win pitchers for a long time pitching right now. I figure that Glavine will get there, Mussina will get close and you can't count out guys like Willis and maybe Carlos Zambrano, but they are all young guys and it will be 10 years before they get close.