I have tried for years to learn exactly what we're doing when we tune using seating depth, both from load development as well as reading the comments of others. I have read numerous posts online that suggested possible mechanisms including fine-tuning barrel harmonics, optimizing how the bullet enters the rifling, or even regulating the timing of how the case neck "seals".
As far as I can tell, it does not seem to be predominantly an issue of barrel timing/harmonics. I base this statement on numerous cases where a given bullet tunes in optimally within a specific seating depth window, regardless of velocity. In other words, loads with the same bullet at velocities of anywhere from 50-75 fps, to as much as 200 fps different all showed the exact same seating depth optima. I cannot completely rule out that by some coincidence that the bullet in each of these loads was exiting the bore at very similar spots in the barrel harmonic cycle. However, that seems pretty unlikely to me do to the wide range of velocities over which I have observed basically the exact same seating depth optimum with a given bullet.
So I keep coming back to seating depth playing a critical role in some aspect of precision that is bullet-specific, such as bullet entry into the rifling, but I really don't know with any certainty what is actually happening. That notion would certainly fit well in the context of bullet ogive profiles (i.e. tangent versus secant) and differences how those bullet profiles affect optimal seating depth windows. One thing I do know with certainty is that tuning with seating depth is not only a critical component of load development with most of the bullets I regularly use, the effect can be very dramatic. In many cases, a single .003" increment is sufficient to go from relatively mediocre precision to shooting one ragged hole. So whatever may be happening when we tune using seating depth, the effect can be very dramatic.