I think a lot more dogs do fine with switching foods than we realize, just because so many dogs do eat the same formula their entire lives, but the consequences when a dog can't handle the transition sure can, uh, leave an impression (and burn a few nose hairs)! So I get why people don't push it.
I like to vary brands and formulas partially because I feel like it gives me more flexibility - because I have a catalogue of brands and formulas that 'work' for my dog, I don't have to worry as much about the store being out of stock, recipe changes, recalls (I still have to worry if my dog is eating a contaminated batch, of course, but I'm not scrambling to find a replacement), or even something being discontinued. I also believe that it's more enriching for my dogs to have variety in their diets, although I acknowledge it isn't necessary and I'm anthropomorphizing a bit.
In general, so long as a food has passed all the necessary testing to confirm that it's complete and balanced, I don't believe that rotating gives any particular benefit in terms of nutrition. However, when questions arise like the DCM scare and the question of whether legume-heavy diets cause problems, I do feel more secure knowing that my dogs are eating a range of diets - some grain inclusive, some not, some heavy in legumes, some not - so if there's a cumulative issue with a certain ingredient being fed over a long period they're a little more protected.
For the record, I personally believe the DCM thing has been blown significantly out of proportion and the actual risk - if there is one at all - is miniscule, although I absolutely support continuing research so we can get definitive answers. But when it first came out, knowing my dogs were on a rotation diet was reassuring.
However, being able to rotate is absolutely a privilege, both because I have dogs who tolerate it well and because I have the budget and access to quality brands to make it feasible. I'll never say it's necessary to have a healthy or happy dog, and in some cases with sensitive dogs or dogs with special dietary needs, it can definitely do harm.