That's not to say that Burger King or McDonald's couldn't do better. I don't really have enough experience with them as a customer or anything else to have a real opinion. But I suspect that, if Burger King were to try to improve their experience in a way that forced them to raise prices by 25% they'd lose a lot of business from people basically just looking for the cheapest burger.
See also the experience of JC Penney and Ron Johnson. A lot of people are pretty much in the position where they have to shop on price.
Keep in mind, though, that if a larger portion of money went to the workers, less of them would be in that position.
It would not benefit Burger King as its clientele’s main goal is purchasing at the lowest price and they will happily go to McDonalds if prices went up. Not all businesses have the luxury of selling to people willing to spend more than rock bottom, and you can see that in most cities, only one or two areas where the upper middle class live will have the business that pay more than the minimum.
If Burger King significantly increased the salary of their workers or otherwise found ways to improve their morale, would it benefit Burger King in the long run? I tend to suspect so, but it would be hard to prove.
The burger joints known for taking care of their people are also usually seen as being pretty good burger places, and that may be causal, but it also may be that they're just slightly "upscale" of the other burger places and also spend more on the ingredients.