Avoiding sugar may still include very sweet fruit varieties, or juice that can still prevent such adaptation... otherwise, sure, you can do similar without full on carnivore. All said, it was an example.
A lot of the problem I have with fruit now is that it's picked so early that it's virtually flavorless. Fuji apples for instance have this beautiful floral/tangy/fruity flavor when they're allowed to ripen on the tree. But go into a supermarket anywhere in my neck of the woods and they're these green things that are just beginning to turn red, and they just taste like fresh leaves with sugar in them. And the supermarket is charging like 4 dollars a pound for the lowest quality crap fruit they can get.
The trick for me is to get them from a grocery store with a huge selection. Among a hundred or so apples, there's usually 2 or 3 red ones. The flavor is amazing.