Except the evidence presented on camera says otherwise. As early as season 1, episode 7 they showed that bullets could hurt vampires enough to put them on their ass, and this happened on other occasions too. Logically, there is no reason you can't pump one full of lead to basically immobilize it and then finish it off with stakes or decapitation. Heck, they also demonstrated that your average demon can die just fine from bullets in Angel.Also, guns are already useless against vampires, which they did explain at some point
It's worse storytelling to demonstrate that everyone in the show, villains and heroes alike, is vulnerable to something as basic and common as fire arms and then have no one bother to use them.
In fact, given that Buffy is set in the modern world, you are basically avoiding a plothole by doing this. Hell, you don't even need an on camera demonstration. Just have Xander ask "Hey, why don't you take a gun with you?" and Giles says "Bullets bounce off vampires as much as they would Buffy." You've now established why you need a designated vampire slayer as opposed to just a government hit squad, or calling in a SWAT team armed with machetes for finishing things off. Buffy and company are too tough for bullets to even slow down, and you need the striking power of a slayer to penetrate a vampire's damage reduction.
This isn't bad story telling, and it does raise the scales. The actual trade off is that now vampires are so tough and dangerous that they would eviscerate any of the Scoobies, and the Scoobies wouldn't be able to scratch their paint. But the show is filled with tons of examples of normal humans fighting vampires with various degrees of success or failure. It was a storytelling decision, not a budget decision, that led to Xander being able to survive Vampire scraps, and Charles Gunn taking them out in groups.
Shows like Being Human had vampires cause massive amounts of carnage off screen, and they had shoestring budgets. They never especially showed Vampires fighting on screen to begin with, but that also neatly avoided the problem of low showings. It wasn't a show about super hero punch outs.
Buffy is a show with super hero punch outs, that simply aren't very impressive on the grand scale of super hero punch outs. (It's also a lot of other things.) Was the budget a factor when they decided to set this power level? Probably. But there were plenty of ways around that if they wanted to be more realistic, more powerful, or less campy.
Hell, they've been publishing Buffy and Angel comics for years now, which would have been a great way to demonstrate this theoretical unlimited budget power level you claim. And yet to do that they gave Buffy an external power up. I've yet to hear anyone name feats that Buffy or Angel use in their default forms in the comics that are drastically beyond their TV show counter parts.