I have witnessed a peahen laying an egg standing up and was 100% mobile during the process. Maybe your assessment of peahens being paralyzed is true with new first year lating hens,or hens passing an unusually large egg but several times when I collect eggs in the evening i've actually seen peahens walking,stop,and drop an egg then fly on a perch,as if they just casually took a poop and moved on.
It was my 3 year old peahen that got egg bound. I'm just telling what her symptoms were like.