I have read that the theory behind the string-through-body as opposed to top is that a longer length string frequency will take longer to decay than that of a shorter length string. Six string guitars such as the 1951 Telecaster and the 1959 Korina Flying V both were praised for better sustain. So the same theory was the approached when Fender and Gibson and other companies starter to build basses. Again the Physics Theory was the science behind the usage. So it must make a difference but, not a discernable enough to notice. Maybe some one can research this further Through patent information submitted by C L Fender in 1951 for his Telecaster guitar D164,227 is the design plan but I could not get any deeper in to find explanation for the string-through-body design.
I have headless basses, and guitars with locking tremolo, and bridge where the strings "ends" right at their speaking length points, as it is. They sustain forever. Can't get the reasoning behind this at all. I think it was Benedetto who did a real blindfold test as he built two guitars with exact specs, but reversed headstocks, and let all strings carry on in different lengths after the bridge and after the nut. No one could detect a single thing, while playing blindfolded even when bending. It plays a little role when using any kind of floating tremolo though on guitars. When bending down the lowest strings does not jump out of the nut slot if the low e carries way past the nut to a tuning post longer up the headstock, i e a reversed headstock. If the low E string ends up wound around a post just after the nut, chances are that it's going UPWARDS (due to slack) at the nut, and when you release the whammy bar it doesn't jump back into the nut slot. And thus the amount of pitch bend that occurs is slightly different too. But that was all that happens. String and metal fatigue is worse with the sharp angle introduced on string through bass bodies as well. So the strings lifespan may be shortented a bit, but not that quite to make it a serious drawback. Mostly on the taught strings like the g-string. The sustain is about the same no matter what. Otherwise my headless basses would just pop and decay within a second. What happens behind the nut and bridge is important though, but sustain, decay is not one of these factors. People often mixes up where a string ends and where the string begins. The overall total build, mass of bridge and nut material as well as overall density wood are more definining factors, and more crucial to the final tone, decay and sustain. But this is slightly OT I think. But I agree somewhat to that "not discernable enough to notice" stance. It's too subtle to notice.
I have not revised my opinion on that. Simply because I've yet to see/hear it on any bass.
