Okay here is anecdotal experience. I had a set of treads on my rear tire at 15/32 while the fronts where at 9/32. Viscous coupled AWD with traction control via four-wheel braking. I first noticed something was up when the car would launch rather quickly. I added an odb-2 reader and saw my AWD clutch was engaging a lot. Thought this was by design due to my heavy foot. Then the clunking started.
The AWD would rather stay engaged which puts strain on the transmission to shift harder. Over time this showed up as increased transmission temperatures. My transmission is sensitive to heat but has a poor design which makes any heat a very big deal. At about the same time I was researching new wheels and determined I could fit 9” wide tires in the rear vs 8.5” in the front. A staggered wheel set would give me more rear wheel power bias, but the closest I could get in tire size was still almost .5% larger in diameter.
In all my research it turns out you need tires of the same size within 3/16 wear of each other to avoid non-full time AWD transmissions from doing dumb things like my car does. You see, the AWD clutch simply engages a power transfer unit and then depends on ABS to control power sent by the differential to individual wheels. That system needs to recalibrate itself regularly and it does this when the clutch disengages. When it doesn’t, all sorts of warnings are tripped (in my car I went down 6 floors of a spiraling parking garage exit at 15-20mph and at the 2nd floor a “service stabili-trak” icon appeared on my dashboard)
In cars with a well designed AWD system this will not happen.. but most cars are not designed to engage in AWD for prolonged periods of time and are really there as a beefed up version of traction control. For instance my Torsen Quattro AWD Audi had full time AWD and never had this problem nor would a Nissan GT-R. But for that fancy Lexus or Hyundai AWD, you may want to make sure you stick to the recommended tire rotation schedule
To end my story, I was at the service center and they mentioned I should get my transmission checked out by the bigger repair bay because of the clunking. I suggested it may be the wear of the tires and they agreed to see if that solved the problem. New set of tires and the clunking, extra AWD engagement, and transmission temps went away.