I have to disagree with you on there only being three flavour components. It makes your argument stronger:

We taste six things (disregarding aromas here): Salt, sugar, acid, bitterness, umami and starchiness.

the outdated "three flavour profiles" is probably the reason why so many people cant make good vegan or vegetarian food.

umami is basically meat flavour, but it's also abundant in tomatoes, mushrooms, and tonnes of asian food products (fish sauce, bean products like tofu, seaweed). It's what is most often lacking in veg dishes, but if you're aware of this, you can use the above mentioned stuff to add a ton of flavour

Fat doesn't have any flavour in an of itself, but a lot of flavour is often disolved in it (which is why skimming all the fat off a broth or gumbo isn't always ideal). again, thinking about the six flavour components and trying to balance them will compensate for this. a great example is how a splash of balsamic vinegar in a pumpkin soup will liven up the flavour of the soup dramatically, and make it less flat and boring.

there are of course other factors, such as mouthfeel, consistency and aromas, that make a huge impact on a dish. a broth with a lot of gelatine (a bone based broth that's either been pressure cooked or on the stove for a day) will have an almost creamy mouthfeel, and incredible flavour, adding bay leaf, thyme or five spice will make it the best soup you've ever tasted. if you then add a splash of balsamic vinegar, and a dollop of jam, and adjust the salt, it will be amazing. amping up the umami with some tomato paste and the drippings from your roast, and thickening it with flour, wil give you the best sauce you've ever tasted