There is, however, the fact that domestic livestock and widely cultivated crops tend to taste the way humans like most because they've been bred to be tasty.
Corn was originally basically like wheat, but they were bred to go from having a half-dozen kernels to having a hundred on a cob by first Native Americans and then the later Americans. Corn is also bred into breeds for having high sugar content (high fructose corn syrup), thick-kerneled corn (popcorn), corn high in specific oils for use in vegetable oils, industrial lubricants, and plenty more.
Pigs, meanwhile, have gone anywhere from having over half their body mass being lard, in the times before vegetable oil was popular and it was the way to grease your pans and keep oil in your lamps, to more modern extremely lean pigs for the most pork chop to the animal and a chance to say that pork is "lean" and "heart-healthy". Meanwhile, there are people trying to breed the pig back into having a "proper marbling" by adding a certain amount of fat back in.
This game's concept of "wild strawberries" is rather ahistoric - strawberries were basically useless to farmers until the invention of the greenhouse, because strawberries were evolved to attract small birds that liked tiny berries the size of one of the bumps on a blackberry. So long as those birds were better spreaders of strawberry seeds than humans, there was no chance of breeding them into berries half the size of an average person's fist you see today. Only after humans built greenhouses did we manage to keep birds out and grow strawberries to our liking.
Basically, there's much greater reason for people to prefer something that is domesticated and grown in bulk and bred for the flavor they produce. Wild meat is often too lean and tough.
Now, with that said, yes, these are non-humans. I'd be willing to say that it could make sense to make different species prefer different things. (Humans crave meat, sugary fruit, salt, and fat because those things have historically been rare. Elves might not care so much about the sugar, however, since they have plentiful access to fruit throughout their whole history in existence, while they might need some nutrients from meat they can only rarely get out of "self defense".)
Beyond that, if 12 types of food is "a doddle", then we could just make it 18 types of food/drink.
That said, I don't think it's terribly necessary to add that much complexity to the supply lines. Honestly, I don't think I had much more than 12 regularly produced food items in any of my previous forts.
I should also say that there are native people who live around the arctic circle who subsist on diets almost entirely composed of marine mammals and reindeer cheese. Even saying that you need to "merely" supply 12 types of food is likely enough to invalidate tundra play. (Or at least, force culling of any dwarf that doesn't prefer blubbery meat or cheese.)
There isn't really that much "challenge" added by forcing players to cater to an overly large number of foodstuffs. It just invalidates any style of play that isn't a trade hub, which shouldn't be a goal.
To go back a second to the flavor profiles idea, one thing that does is allow cooking with extremely flavored ingredients to balance out a flavor profile, and hit a target flavor without necessarily dictating a particular type of food. That is, if a dwarf really likes sweet things, you can either give them fruit, or if you have tons of eggs and meat but no surface fruits, you might just marinate their steak in tons of dwarven syrup to sweeten their meat enough for them to like it.
Provided flavor profiles is made in conjunction with cooking rewrites, you could introduce spices that do not serve as direct nutrition, but simply alter the flavor profile, (or maybe cause minor beneficial syndromes in the case of some herbs and spices, like ginger,) so that you can push a food from one flavor category into another. That would keep the flexibility of diet while still satisfying a need for some form of diversity of diet.