Re: Why do people like single cutaways?
Many people believe the sound improves.
The issue is a little fuzzy since there are very few guitars that are only different in single or double cut. Gibson for example, both with the LP standard and the LP Special, gave the double-cut model an entirely different neck joint, further up the neck, and in the case of the DC standard it also got 24 frets which changes everything.
Many double cuts are also thinner, the SG versus the LP is the classic example. The double cut is the least of the differences here.
Myself, I believe in a "wood sound railroad lines" . I think that acoustically great sounding guitars are lucky that the grains are cut in a way that they transport sound end to end and have no dead ends just killing parts of the sound. Then, the thinner your body, your neck or your neck point, the bigger the chance that you killed it. For example, a thin neck LP can come out amoung the best sounding LPs. But statistically it seems that thicker neck LPs come out great more often.
Similar, thick body Les Pauls seem to have a higher chance to sound good than thinner bodied guitars of otherwise similar construction. A thin neck joint might be OK but raises your chance of "cutting the rails".
Just my two cents.