Isn't the purpose of the wrist twist to lock the wrist up and take out the slack so you can use it to connect to the core (via the elbow then shoulder, etc), more or less? In which case uke making their wrist stiff does part of your work for you and you can just skip that step...?? Why would it make it harder?
Not everyone applies kotegaishi in this manner. Some practitioners treat it more in a manner which I would call kokyunage, where they are drawing uke's wrist away from their center, then about/above shoulder height, then out away and down. Hard to explain, and rough to fall from.
Generally I apply wrist manipulations in the manner you are talking about (vice pain compliance). A good training tool is having your uke stand, make a fist, stand statically, and hold their arm solidly as you try to apply kotegaeshi. You probably won't be able to get everyone in your dojo, but its good training and helps understand how the actual technique works. This is interesting practice because you will (or should) meet much resistance and failure while expending a lot of effort. When playing around with your micro-adjustments, you will happen upon the 'sweet spot' (to borrow a term from the nikkyo thread) and uke will drop unexpectedly, quickly, and effortlessly.