A student may withdraw for a number of reasons, including time constraints
Yes. Which would otherwise be a F because they'd be unable to attend class or whatever the case.
GPNC exists is to protect your G.P.A.
Yes. Precisely. A "W" is seen as covering your ass MUCH more than a pass/fail. People rather see "oh they didn't do as-well as they hoped in that class (GPNC)... VS. Oh they were a complete screwup in that class and took a W."
student sets the threshold for credit to be assigned
Yes. Failing to meet an ambiguous threshold (which isn't on your transcript) is easier to explain than a "W".
Other institutions who do NOT use a similar system or a GPNC system typically will assign either a C grade to a P grade, depending on the institutions equal, or a F for a NC grade, if calculated into a student's GPA.
Which is why as SBU students we are lucky that GPNC exists. We have the opportunity to explain a NC grade rather than having a "C". If what you say is true.
... GPNC is better than withdrawing ...
It is. Ask your advisor. Which is why GPNC is more exclusive and only offered for some select classes, while withdrawing is open to all classes.