Well for one, the elbow is pretty tempting as a target as you just mentioned. You're still held by the wrist and the elbow (stiff) is right in front. In any case, an Irimi nikkyo is still quite possible with the stiff arm.
Bending the elbow allows you to get in closer. If nage is applying torque into himself (sensei points this out) you can go into his groin with an uppercut, or blend with that motion.
So I see that ukemi as a better alternative to the one where I end up exposing my ribs because of the stiff elbow.