At first blush this seems to make a lot of sense, but if you look at it too closely the abstraction inherent in hit points and saves breaks suspension of disbelief. i.e. Hit points suddenly becomes literal wounds dealt by specific sword blows. There are 3 saves reflex, will, and fortitude, and they literally and in a direct and visceral way represent 'getting out of the way' 'resisting with your mind' and 'enduring with your body'.
But wait - you made that reflex save and you're still standing up? You failed that fortitude save and didn't fall to your knees? When the saves represent literal specific things then it breaks suspension of disbelief. The 'three categories' of saves also seem very trite and videogamey.
But what of old school saves you say? Abstraction, and this indeed is why they are cool.
A Dungeons and Dragons old school game is not like a aerial-view action RPG that we are simulating with dice—good gods, it takes hours to fight a single combat that way. Instead it is much more like the surface of an atom. We have a general idea of what's going on down there, and we get bursts of specific information (say location OR velocity) and we use our imagination to draw the rest in our minds.
Take old school saves for instance. Paralyzation/Poison/Death magic, Rod/Staff/Wand, Petrification/Polymorph, Breath Weapon, and Spells.
But what do these mean? What do they represent?
Why that's the coolest thing about them! Nothing specific at all! All we know is success or failure—the actual means of that is up to you. (and your classes general ability to handle that specific kind of threat is built into the numbers)
Let's say your wizard makes a save versus spells—he inscribed arcane counter-spelling runes in the air before him to disperse the magical energies.
Let's say your paladin makes her save versus breath weapon—she holds her shield up and her gods divine grace splits the fire of the dragon in either direction.
Let's say your thief makes his save versus rods/staff/wand—he holds forth his reflective amulet and the beam hits it and bounces away.
The point is, that the game doesn't tell you how you make your save—that's part of the discovery of what's happening and the fun. Logistically it's a lot more fun to come up with answers for why things happen then trying to plot out a specific sequence of events that is occurring every six seconds. Also, you've got a lot more room for awesome and rule of cool in your descriptions.
So how to decide which save to use for a trap? Paralyzation/poison/death magic has to do with 2 things—toughness and divine grace.
Rod/Staff/Wand has to do with rays, artificial magic generation, and device based effects.
Petrification/Polymorph has with emotional and physical resilience. Self-control is a big factor here.
Breath Weapon has to do with area effects, luck, and grace.
Spells is a catch all category and the general domain of magic.
Clerics have the best saves versus paralyzation/poison/death magic.
Mages have the best overall starting saves and the worst high level ones
Fighters start off with the worst saves (by far) but eventually have the best saves.
Thieves start off slightly better than fighters, but end up slightly worse at 20th level.