In signal detection theory, people often use $d'$ to assess performance. Apart from the fact that $d'$ is in $z$ units (units of measurement transformed to standard deviation units, i.e., $z$ scores), making it comparable regardless of the original units of measurement. I can't see what the advantage in analysing $d'$ instead of proportion correct is.
Don't both account for bias? Would they follow the same shaped ROC curves?