What is the difference between a paired sale and a simple "regression"/best fit line with the same data? Graphically, they will be identical and the regression line would suggest an R2 of 1.00, perfect. So, by relying on two or 4 or six pairs will in both methods suggest nearly identical results. The regression analysis includes some measures of how sound the results are, whereas those using the same limited data for paired sales or sensitivity analysis just assume greatness without question.
Results improve with multivariate regression. In my experience, those most vocal and adamant against "statistics" and "regression" are the least likely to have learned how to apply it and gauge the results (to the point, in my opinion, of not even having tried). There is a lot of ground between all and none, but current trends suggest that appraisal work is showing heavily toward the all stats approach. Of course, "they" probably don't have a clue, either.