So I saw this movie for the first time as an adult and what I didn't notice as a kid is how damn twiggy Jafar is. Is there a reason someone so powerful and rich has a holocaust survivor diet? Look how fat the Sultan is.
You said it was popular for villains, but there are many cases where it isn't used, so Jafar's thinness seems more chosen for him particularly than part of a general trend.
The unused Jafar song Why Me opens with "In my formative and hungry years..." which suggests he grew up with little food, that may explain his scrawniness.