Does a term exist for this concept in statistics? Suppose you have a dataset where the covariates are biomedical information for a given patient (e.g. height, weight, blood type, etc.) and the response variable is whether the patient has a certain disease. You are interested in making a classification model that will help screen patients in advance for this disease (i.e. save time and money).
Suppose you are able to create a decision tree that produces decent accuracy - but the "rules" produced by the decision tree are not very "helpful".
For example: if height between (150, 180 cm) and weight between (150, 200 lbs) then disease = true.
Suppose this rule proves to be a very accurate rule (i.e. when this condition is true, patients almost always have the disease) - but it's deemed too vague by the doctors to actually use. Instead, the doctors prefer to spend money/resources and physically screen patients.
Is there a term for this in statistics? An accurate model which is deemed too arbitrary to use?

You state

Suppose this rule proves to be a very accurate rule (i.e. when this condition is true, patients almost always have the disease)

But that is often not the situation. If the broad boundary is very accurate, and if the detection means almost certainly that the patient has the disease, then this is a very good decision rule. The doctors will be happy with it.
The situation is more like below:

*

*Broad boundary:
This detects most cases, it is sensitive.
But, it is not accurate. Often the detection is false and the person is not sick.


*Narrow boundary:
This is accurate. If it makes a detection then often the person is also really sick.
But it is not sensitive. It is missing a lot of cases.


Is there a term for this in statistics?

There are many terms for this. See this wiki article on 'Sensitivity and specificity'.
