The moments that call for a saving throw represent the pinnacle of tension in D&D. They lie at the crossroads of defeat and success, of life and death, and can be the culmination of an evening or a year's campaigning. So why are we rolling a die at this high point? Why are we leaving the resolution of our shared time to random chance, no matter how intelligently or recklessly the game has been played?
The moments that call for a saving throw represent the mundane points of D&D: a pit placed in a hallway, a random trap rolled off some table, or the effects of a harsh environment. Again, random chance takes the place of smart/careless behavior and turns these aspects into something resembling adventuring attrition.
Saving throws are overused. When I first talked about taking attrition damage during overland travel, one commenter wanted to add a save to avoid a day's damage. Like you can really avoid the effects of the environment by being bad-ass? More likely, he was calling for saves because the PCs are precious and should be afforded every opportunity to survive/thrive regardless of smart/reckless play.
Well, the real reason saves are overused is because D&D is under-designed. How many mechanics are just rolled up into a saving throw? Spells, abilities, effects, poison, traps, magic items, the list goes on and on. Just throw a save on an action to create a lazy mechanic to adjudicate its effects. It isn't even a robust and elegant mechanic that could be applied to numerous situations; it is just lazy. Maybe the original designers ran out of creative steam and then we all just kind of turned a blind eye to this gaping hole in the game's mechanics. Or maybe we are blind to the failings of tradition.
Either way, saving throws are a boring, lazy, static mechanic that form an umbrella over countless actions and opportunities in game that could have mechanics designed to add tension, flow, and enjoyment to the game.