I have actually built a couple of straw-bale buildings. For myself and others.
The short answer is "Yes, you need some type of breathable finish on it.
The other parts are not so simple. Yeah, you could shot-crete it. Yeah, you could build stud walls and rock them. Yeah, you could use tyvek.
But why?
It is a proven technology that has stood the test of time without shot-crete, furred out sheet-rock - or even in-filled timber framing.