Saves are a fairly new stat and back in the 70's closers (like Gossage) would pitch 2 innings quite frequently.
A guy like Mo pitches what 80 innings in a year ? A workhorse starter ( like CC) will go 250+ . Closers have it easy. They should be "stoppers" and brought in anytime after the 5th inning when the situation calls for it. Like say the starter starts to lose it in the 6th in a close game and loads the bases with one out....then bring in your "closer" to "save" that situation ( and pitch the 7th) instead of some bum out of the pen that will give up runs.
Pitching just the 9th when ahead ( a save situation) just intentionally inflates that save stat, use your best reliever ( the closer) when most needed.
Rivera's record will be broken, he was great, but I'd use my pitching staff, as a staff if managing and not hesitate to put in the relief ace when most needed. There is no game to save if the bum pitchers in most bullpens relieve the starter with runners on.