I view flavor profiles in terms of the 5 basic flavors, but, add the characteristics of known flavors, similar to the worlds of wine and beer. You seek out the familiar when tasting, those 5 basic flavors are a start, but, sweet means a very different thing from milk chocolate, salty is not the same as sea water, so I find that providing both terms to be useful when trying to communicate flavor. I rarely try to communicate the flavor of BBQ in these terms, although, I can see where these terms could be useful in a situation such as this forum.
I think if I received a review of my BBQ and it said the flavor profile was sweet, I would be disappointed, that is not a flavor profile, that is one useless description and not a flavor profile. A flavor profile would be more like, the ribs were sweet with hints of honey and caramel and a backbone of savory spice of black pepper and roasted garlic. That would tell me that they cared about their taste and my feedback.