hobodave's answer is most of the way there but I think it understates the importance of protein toxins. With the vast majority of foodborne illnesses, the bacteria aren't particularly harmful at all; what you need to worry about is the protein toxins they produce.
E.Coli - probably the most well-known form of food poisoning along with Salmonella - is actually a harmless bacteria that already lives in your lower intestine. But there is a particular strain of E.Coli, notably O157:H7, that is primarily associated with food poisoning. The reason? It produces what's called a Shiga-like Toxin.
E.Coli contamination is actually dangerous on two fronts. Because the bacteria are so well-adapted to surviving in the human digestive system (as I pointed out earlier, that's their primary habitat), ingesting even a relatively small number of the bacteria will result in them multiplying and producing those toxins in your gut (and the rest of the way down). This is why it normally takes several days for you to feel the effects of this type of food poisoning; that's how long it takes for them to produce the toxins in sufficient quantity for your body to notice.
But they don't need to be in your gut to produce those toxins; a piece of meat at room temperature provides good enough conditions and more than enough raw material for them reproduce and emit those same toxins. So if you leave it sitting out too long, then it really doesn't matter how many bacteria you kill, you are going to end up with E.Coli poisoning fast, because you don't even need to wait for them to produce the toxins; they're already there.
The problem is that you can't "kill" a protein toxin with a brief burst of heat because a protein isn't alive. It's just a protein. The temperatures and times needed to destroy that toxin would be similar to the temperatures and times needed to destroy all of the protein in the food, draining all the nutrition value and quite possibly turning it into a lump of charcoal.
Salmonella seems to be a fountain of misinformation with all sorts of people saying that it doesn't produce toxins. This simply isn't true. Inside the host it produces what's called an AvrA toxin (which isn't "toxic" per se, but allows the bacteria to grow to larger numbers), and some strains can also produce a CdtB toxin, which is highly toxic. (Apparently there's also a similar toxin produced by other strains.) I'll be honest, a lot of the medical mumbo-jumbo is way beyond my ability to comprehend, but it seems that a lot of the public confusion comes from the fact that salmonella can do some nasty things even without the toxins - but that doesn't mean that the toxins themselves can't do plenty of damage even if you manage to kill the bacteria.
The same applies to many other types of dangerous bacteria; C.diptheriae produce the diphtheria toxin, C.botulinum produce the botulinum toxin (botulism); even the infamous mad cow disease was, as far as we know, caused by a protein, not a bacteria, which is why it was able to be transmitted to humans even through cooked beef.
Are protein toxins the only reason why the USDA insists on a maximum 4-hour cumulative danger zone? Probably not. As hobodave says, the more the bacteria multiply, the harder is to kill all of them, even at high temperatures. The figure of 74° C / 165° F that the food agencies give us for poultry is not going to kill exactly 100% of all the bacteria, and if it only kills - I'm just throwing out a number here - 99.999% of them, that may be good enough for relatively fresh poultry but won't be enough if you've got a whole bacterial colony to worry about.
We can only speculate as to exactly what's entailed by the "danger zone" but my guess is that it's actually a combination of statistics, probabilities, and safety margins, which include, but are not limited to, the effects of protein toxins.
Best Answer
Low and slow is best for certain types of dishes and certain cuts of meat. Meats that have a higher percentage of connective tissues in them come out tough if you don't break that collagen down. Extracting that also adds depth and richness to the dish.
Cuts that are just the muscle and marbled fat, on the other hand, don't really benefit from that. That's why the stews and soups you mentioned, where you are shooting for a rich melange of flavors, call for those cheaper cuts.
A burger, steak, stir-fry would all come out bland and relatively flavorless using that method.
Now, sometimes there is a variation on this to more evenly cook the meat - Cook's Illustrated has a method where you cook a thick steak in the oven at a low temperature so it's evenly cooked to medium-rare throughout, but then you finish the steak by searing in a hot skillet or pan. The idea there is they want the sear, but they want the maximum amount of meat throughout to be medium rare and not be well-done/grey.