Those who spend a lot of time typing on a computer keyboard or playing on a music keyboard (piano, ..) learn that their wrists should remain as straight as possible. The idea is that the tendons that move the fingers go through a tunnel inside the wrist (the carpal tunnel) and if the fingers are moving incessantly for hours, then any angle will make the tendons rub against the wall of the tunnel. The tunnel will get inflamed (carpal tunnel syndrome) in the same way that moving a cable against the edge of a wood tabletop will make a groove in the table, and fray the cable.
Cyclists with no history of wrist pain are just as prone to wrist pain on a bike. This suggests that the pain does not arise in the carpal tunnel at all.
I do try to move my hand location frequently, but I also like to maintain a reasonably high cadence since I then pedal with the least effort. The need to shift constantly means that my hands are almost always on the hoods, and that I seldom use the other four positions.
Even folks who are regulars at the gym may have no way to eliminate having "weak wrists". The following is wild speculation: one workout or another may strengthen the muscles around the wrist, but nothing can make the wrist joint itself stronger.
I'm familiar with the few exercises that rehabilitate carpal tunnel syndrome and that prevent its reoccurrence, but on a road bike I can confirm that the pain does not even arise from the carpal tunnel. I'm shifting often, but nowhere near as often as the number of keys pressed during a typing session (yes, yes, such as this one). Also, the pain from the position on the handlebar is not nearly as bad as carpal tunnel pain. The latter is nasty because as soon as it is slightly inflamed, the pain quickly gets worse; maybe because there is less room for the tendons to move freely. The pain from the handlebar goes away after about 24 hours, whereas carpal pain can last weeks, or longer.
I've experimented with moving the seat tube up/down by 2-3mm at a time and this seems to be successful at identifying the most comfortable height.
After experimenting with multiple rides in each of two rotational settings, I'm now about to start iterating to turn the angle of the handlebar until I identify the one that makes my wrists as straight as possible, but before I experiment, I thought I'd ask the collective wisdom here.
Is adjusting the handlebar angle a viable way to reduce wrist pain? As you see in the picture below, I have so far adjusted the handlebar angle looking after the comfort of my lower back (another weak spot that I need to watch out for), turning it up. I'm assuming that they labeled the zero line to give us a hint that we may want to start by centering that zero line.
Edit: Aligning the zero line of the handlebar (horizontal axis of the circle) with the center of the stem (red line) made the hooks position too painful for my back. My solution has been to turn the handlebars up (by about 6 degrees, which turned out to be surprisingly a lot). This +6° solved back issues, but now my wrists on the hooks are abnormally turned up, and, sure enough, this leads to wrist pain–even after multiple rides to allow for the invevitable first-couple-of-times-pain. My question, briefly, is whether to iterate (binary search?) to find just the right angle. End Edit
If the frame is too large for me, then making my wrists and my back simultaneously comfortable may be a losing battle. I could seek that perfect angle all I want, but one or the other would be unhappy. The frame feels just about right (do even professional cyclists have access to custom frames that fit their bodies to the millimeter, in the same vein that professional skiers have access to custom-built boots? But I digress). Turning too far forward/down will make my wrists happy, but strain my back, and vice-versa. Seeking the sweet spot may be just a compromise to increase comfort, or at least to decrease the pain.
It would have been nice to have some graduation to read out the angle directly without having to add hand-written notes, but that gripe also applies to the seat tube, and so we can leave these issues to the constraints of fast factory production lines.
Just to clarify, the added context made for a long question, but your answer need not be long. If you can confirm "yes, finding the right angle is a compromise" along with a bit of experience, that would be a good start for me.