To me the answer to the question, as posed, is:
I don't vary the nutrition of my fish. Other than nutrition at different stages varying slightly, such as fry or young growing juvies benefiting from slightly higher optimal protein levels, or minor differences between certain types of fish, the nutritional needs of fish are consistent. In other words, whatever you feed, your fish need the same nutrients and this doesn't vary, so there's no reason to 'vary fish's nutrition' in that sense.
As far as what some hobbyists theorize is the need to vary their feed in order to accomplish good nutrition, I agree with comments already made. If you're feeding a balanced/quality food in the first place, there's no need to do this.
Do fish get bored eating the same thing consistently? That's debatable-- doubtful imo. I don't think anyone imagines that a whale shark gets bored with eating krill every day or that a tropheus scraping algae/bio-film off rocks in Lake Tanganyika thinks to itself "this is getting boring". I suspect if they're finding enough to eat and whatever it is tastes good to them they're pretty happy, whatever happy means to a fish.
Do fish like to get a good tasting treat from time to time? Heck, yeah from anything I've ever seen. Or some fish seem to respond to certain treats or supplements to encourage them to spawn (example is my wild angelfish seem to spawn more often when I give them freeze dried blood worms).
But as far as needing to be fed different foods for the sake of basic good health, not really, not for the vast majority of fish. (Only possible exception I can think of might be an unusual or rare fish that needs and gets some unusual nutrient in it's specialized wild diet and somehow doesn't get that nutrient from a good commercial fish food.)
But is it frowned upon to feed more than one type of staple food? That becomes a matter of opinion regarding the specific foods you're feeding. For example, I'm not too high on Hikari foods in general and I don't use them anymore (after food testing I did years ago where I had better results from other products). Not that I actually frown upon someone using Hikari foods, just not personally impressed with them.
