I'm not disagreeing with what you say here, but I think we're arguing about subtly different things.
E.g. you'll note my zebra example was not about whether one should additionally request a photo of the animal just to make sure it is indeed a rare animal. It was arguing that given existing differentiating information that points to an uncommon condition in the first place, one should not dismiss this on the basis that horses are still more common than zebras in the general case regardless. Under this uncommon information, the prior of thinking about horses should go out the window, and one should absolutely focus on zebras (at least as an additional differential). I assume you would also agree with this conclusion.
But of course, in real medicine things are not as simple as this contrived example. So the point I'm making is that, from what I have observed, there seems to be a bias towards decisions based on "prior" rather than "posterior" probabilities, even in the presence of additional differentiating information which should have prompted additional differentials to be considered. But this is different to saying one should constantly seek additional evidence to include or exclude additional differentials that are unlikely in the first place. That, I agree, would be a waste of time and resources (and potentially harmful for the patient).
Having said that, I somewhat disagree with the phrasing that we should not be ordering tests if we aren't ready to follow their results to the logical conclusion. This is a bit like saying, "I don't want to check for X because if I do and it checks out it will derail my current management plan"; but then this is putting the cart before the horse, since it's the findings that need to dictate management, not the other way round. I do think it is reasonable to say that one shouldn't be ordering a test if the expectation that it will change management is sufficiently low to justify the time/cost expended for it -- and where this expectation is a function of both the likelihood of the finding (given current information!), as well as its potential to change management. But this doesn't mean that if you do find an unrelated inconsequential incidental finding you are now required to divert all resources to it.
Conversely, if an incidental findings does prove worthy of treatment, then I don't see the problem with committing to treat it, as long as you don't lose sight of the original complaint either. Obviously that doesn't mean one should go looking for incidental findings willy-nilly though.