This is my answer to students who ask about wrist pain while doing back bends: "The site of the pain is not the cause of the pain". They often want to know what they can do to stretch their wrists. First I usually ask them to bend their wrists back so that I can see how much range of motion they have in their wrists. If they have normal range of motion and no injuries to the wrist, then the wrist is not the issue. I don’t usually have to see them do the pose to know that their arms will not vertical when they do wheel. When the arms are not vertical in wheel, the wrists will be bent at less than 90 degrees and that is not in the normal range of motion for the wrist and therefore not very comfortable.
However, just to be sure, I always ask them to do their pose for me so I can see if there is anything else going on. But more often than not, their arms are not vertical.

Here is a picture of me doing wheel where my arms are pretty vertical:

Here is a picture of me doing wheel where my arms are not vertical.

Observe the angle at the wrist. Which one looks like it hurts?  Ouch!  The wrists aren't meant to bend that way!   If the shoulders aren’t open, the lumbar spine doesn’t bend or the quads and/or psoas are tight then other body parts will have to compensate.

In the final form of the pose Wheel should look like an upside down “U”. When it looks more like an arc of a circle, then there is more shoulder or hip opening that needs to be done and the wrists should be supported; either on blocks, the wall, someone’s ankles or even a tightly rolled up blanket placed against the wall can work.