Most BBQ sauce recipes specify that you cook them, why is this? Would it not suffice to just mix the ingredients together as they will be cooked when you use the sauce on the grill anyway?
Most of the popular ingredients for BBQ sauce (vinegar/ketchup/sugar etc.) tend not to mix very well together. I know whenever I've made BBQ sauce, placing all of the ingredients into a pan together they tend to separate and are difficult to combine.
Heating up the ingredients, however, causes them to combine better, and after a short time cooking they will bind together and give a more consistent texture/taste. Otherwise the different ingredients may continue to separate even when mixed, and you may find clumps of sugar that have not dissolved into the liquid etc.
It's quite possible your BBQ sauce recipe doesn't need cooking, so long as things are substituted (like sugar for sugar syrup or honey) in order to combine better, but this may well give an incorrect texture because of the change in ingredients.
Therefore if the ingredients you use can be combined without being heated, it's likely that it doesn't need cooking, however you may end up with an uneven flavor.
As pointed out in a comment by @ToddWilcox, there may also be constituent ingredients that do require cooking, such as garlic or onion, in order to achieve the correct flavor so that they do not taste raw.
Some sauces may also specify being cooked simply to make them thicker or more concentrated, as adding thickening agents such as flour may affect the taste, particularly if it is uncooked.
So whilst there are some BBQ sauce recipes that may get away with being uncooked based on their ingredients, there are others that will definitely require cooking.
There are some sauce recipes where you need to thicken them to the point where they'd stay on whatever it is you're grilling. If you didn't cook them down, they'd have the consistency of a marinade, and just drip off.
Sometimes you need to evaporate out some of the moisture, but other times you're actually creating chemical changes ... cooking sugar to a new stage in the case of most barbeque sauces. For starch thickened sauces (not as typical in barbeque sauces), you'll often need to bring them to near a boil so the starches will start their thickening.
As barbecue sauces may also be used cold (after you're done cooking / when serving), it's also not guaranteed that it'll get cooked otherwise. In those cases, even if the sauce is a bit viscous after mixing, you might warm it to help the flavors blend better.
Most sauces that I make require cooking because they have sugars that need to be heated to blend properly in the sauce. Spices that are added also need to be cooked to blend into the sauce evenly. BBQ sauce is mostly added at the end of the cooking process or at the table as a condiment. If it's not cooked first the spices and sugars would give the sauce a raw flavor that I'm sure no one would enjoy.