If you start out with the idea of an all powerful Christian god being the reason the holy symbols work, it seems a bit... underpowered.
I mean in AD&D if you're a high enough level cleric you just destroy undead from a distance, whoosh, bit of prayer and they're all gone.
Reckon that would work in the Buffyverse?
If there are a whole bunch of powers competing, then it makes a bit of sense - cross-power and vamp-power get in a fight, cross-power has a bit of an edge so gets that cowering effect, but vamp power fights back.
But if any one deity is supposed to be omnipotent... well, basically you're back to the problem of the existence of evil, only more so. Because supernatural power is pushing back supernatural power, so god is doing something about it, but not a whole heck of a lot.
So you end up with the idea, god doesn't actually want to destroy vampires. On account of, if an omnipotent god wants to destroy something, then destroyed it is.
So why does that god want vampires around???
Why smallpox, basically. Ends up a tricky theological problem.
If you start with a whole bunch of smaller and more specialised godlikes, then the problem is different. Antibiotics are specific, and the other dudes are finding ways out around the edges all the time. Or, theres a goddess can keep vampires from your door, but the only goddess of vampire slaying is incarnate.
And the cross and holy water thing? Well, they might not do much more than plain old stakes, but the bit more they do is enough to save lives. In ways that don't kill anyone, which seems appropriate for a god with a bunch of commandments about don't kill and turn the other cheek.
But if its meant to be non-violent, why does it burn?
I have this theory that actually, its not god doing the ouching at all. It is the demon, rejecting god. Wouldn't do to let Angel get too close to all these redemption symbols, might get away from the demon. So make the body ouch, to keep the soul in the clutches of the demon.
All this being not particularly canon, just wandering around speculations.
And the reason it isn't in canon is because the parts that are important to us are the choices the characters make. Crosses and holy water are tools to them. As soon as we start getting into what gods are doing, what choices gods make and what their priorities are, then gods become characters. And then they have to get written in in interesting ways. I guess somewhere around then you end up with Hercules or Xena. Not that I've watched much of either show. But the gods are players there, making choices and stuff, so they're characters.
If we want to concentrate on like Buffy and Angel and such, the gods don't be being characters, any more than like the president would be. Any more than the dude that makes the guns in action movies. Because they aren't who the story is about.