Why is not overlap in covariate distribution a part of model diagnostics? I often compare groups that appear not to be comparable when viewing their descriptive data. For example, I frequently compare mortality risk (with Cox, logistic and Poisson regression) among individuals with and without a specific exposure, which can be hypertension for instance.
Now, when viewing my baseline tables, which convey some sort of descriptive representation of the groups, I often note that the groups are very, very different in terms of key variables such as age. The distribution may differ so much that I actually wonder if there are enough sufficiently comparable individuals between the groups, in terms of age.
So what I did was perform a matching to find comparable individuals which revealed very different results. I'm not saying matching is the solution, but I wonder why is this assessment not an integral part of regression modeling? How poor can regression perform in these instances?
 A: The key idea to bear in mind is that you are describing observational data.  What your results will inform you about is the marginal association between your exposure and your response.  That is it.  Whether you use matching or make a herculean effort and find groups that are more similar on your measured covariates, you will still only ever have the marginal association.  So regression methods will give you the right answer to a certain question, the issue is whether people realize which question regression methods answer.  
From a different perspective, as your groups overlap less and less on your covariates, your variables (and your exposure variable in particular) will become multicollinear.  That means that its standard errors will get wider and wider.  The model is telling you the marginal association between the exposure and the response when people have the same values on your covariates.  Since there aren't any people with similar covariate values between the exposure and non-exposure groups, the model is more uncertain about what the true value of that marginal association is.  So the SE's and confidence intervals get correspondingly wider.  In that sense, the model may be less useful for you, but it isn't incorrect.  
