"Of course, I'm assuming the player doesn't practice save scumming."
Part of the problem is that right there. A lot if not most of players do in fact do that.
The fact that they do is part of the problem, if a person wants a good, strong, story. A character's success or failure in that story ought to depend on preparation, planning, good tactics, and story needs, not a random dice throw.
Really, I guess this problem is built into the D&D D20 system, especially where saving throws are concerned, but also, to some extent, where chance to damage is concerned.
How many insects or rats would it take to kill you, a human being, even with a swarm of them with very good luck attacking you? Basically, no realistic scenario would allow any realistic number of insects or rats to seriously hurt you, unless poison were a factor, or unless you were in the jungles of South America and facing swarms of fire ants or killer bees.
Any individual first level character of any race amounts to a single, individual insect or rat to a dragon, a god, or an epic level character of any class.
The whole idea that *anyone* of any level should have even "a snowball's chance in Hades" of doing more than scratching a being on the level of a dragon or a god, or even a heavily-armored high-level fighter, is one of the places where Gary Gygax went wrong when he created the entire system.
I very much like disabling the "automatic failure on a roll of one" rule from the system as a way to greatly increase realism, and rewards for playing the game intelligently.
"Automatic success on a 20" is fine for any kind of attack roll, even though the damage from that "critical hit" might be negligible against gods and dragons.
"Automatic save failure on a 1" is not fine to me, not in a game with save-or-die spells in it, which is supposed to be a framework for good storytelling.
Getting saves so high that the bonus finally reaches 20 is not something any character can do easily. That character who desires save bonuses of 20 will have to spend its lifetime working on that save bonus, and collecting magic items that help with the dream of having 20 save bonuses, or else to advance to such high levels that it becomes a god. There should be a reward for focusing efforts in that direction.
The idea that a mere mortal has a chance to land a save-or-die spell against a god is ridiculous to me, or at least, it lends itself to very, very bad storytelling.