I can't think of a single reason. I've never rigorously tested anything like this, but I've seen too many tiny groups shot by secant ogives (and aggressive ones at that - like the Berger 90) to believe there's much disadvantage to using them. I might even begin to wonder if this isn't just urban legend, or perhaps something related to a special case rather than generally true. Maybe even just a matter of perspective blown out of proportion.
But to even start to answer that question, we need to know who seating depth impacts group size to begin with. I'd argue we don't really know. My own speculation is that when the bullet is released into the bore, it happens with imperfect balance, which starts the bullet to yaw in a cyclic manner, which gets straightened out by the freebore. The seating depth, therefore, determines the point on that cycle that the freebore takes hold. If the bullet is already pointing relatively straight, you have success. If not, there's some deformation or tipping that adversely impacts precision. Jamming into the lands, of course, allows for no oscillation, and tends to help by ensuring that the bullet is straight - if the lands are not worn asymmetrically.
Unfortunately, this doesn't do anything to explain why a secant ogive might be more sensitive.
Obviously, that's all made up and I have no idea how you'd even try to verify it as true. But I can't think of much else that would cause such a dramatic impact from such small changes. If people can reliably document a cyclic pattern in seating depth, that might be a start. If not, back to the drawing board. I've never really tried.
The one clear fact we can all agree to is that seating depth can, in fact, have a huge impact on precision/grouping. Even very small changes can show this effect. In my hands, groups will generally go from mediocre/poor to good, or even outstanding within a single .003" increment once you are "in the optimal seating depth window".
My gut feeling tells me seating depth is about barrel timing, but I cannot currently
prove that to be true. The argument against it being a barrel timing effect is that such a small length increment relative to overall barrel and/or cartridge length is insignificant. However, it is important to remember that during the time the bullet is traversing the rifle's freebore, it is not moving with anywhere near the velocity it will have when it exits the bore. So even a very small distance increment
could have a significant impact on barrel timing. If this is the case, one would expect seating depth to follow a cyclic pattern over a large enough window; i.e. tune in and tune out with a repeating pattern. I agree with Damon and Laurie's thoughts above that it would be interesting to test a very wide seating depth window in very small increments. The problem with this idea is that such a seating depth window is large enough that dramatic changes in pressure and velocity would be encountered. So it would be critical to actually adjust charge weight in order to maintain relatively constant velocity/pressure over the entire seating depth test window. Basically, you're talking about a huge amount of time, effort, and components to carry out such a test, which is probably why it isn't commonly done, even though it's possible if one was sufficiently motivated.
Another potential effect of seating depth is with respect to how the bullet engages the lands as it enters the bore. I can easily imagine how differences in the relatively smooth transition between ogive and bearing surface found in tangent ogive bullets versus the rather abrupt transition found in secant ogive bullets might have a significant affect on precision with regard to how the bullet is positioned relative to the bore axis when it enters the rifling. In the case of the 90 VLDs as Damon referred to above, a large number of folks are currently using the PTG 223 Rem ISSF reamer that cuts 0.169" freebore. In my hands, 90 VLDs in two different chambers cut with this reamer always seem to tune in at either ~.004-.007"
into the lands, which is a fairly narrow optimal seating depth window, or starting at ~.018" to .021"
off the lands, which seems to be a much wider optimal window. It is important to note that the freebore cut with this reamer is only about .0002" over bullet diameter. For some time I have heard common [anecdotal] wisdom regarding VLD bullets to the effect that they like to be started into the lands and may not shoot well when jumped. Although there are many examples suggesting otherwise, such wisdom stills seems fairly commonplace. One possible explanation why the 90 VLDs can be tuned both into and out of the lands could be that the very tight freebore cut with the 223 Rem ISSF reamer simply doesn't allow the bullet to do anything but go straight into the bore/rifling along the freebore and bore axis (i.e. with minimal yaw/pitch). However, I am currently also testing a new (to me) 30 cal VLD bullet in a rifle that does not have such a tight freebore. This bullet seems to shoot optimally at .006" to .009" off the lands, so clearly there are examples where VLDs don't
have to be seated into the lands.
The bottom line is that it is probably possible at this time to determine experimentally what the effect(s) of seating depth are with respect to precision. However, such tests are probably not easy and not cheap in terms of time, effort, and components. So even though I'd really love to have more definitive answers on the topic of how seating depth affects precision, I'm personally just going to continue doing straightforward seating depth testing, which I know from experience will give me sufficient information for load development, even if it doesn't reveal any deeper insight into the "how" and "why" of seating depth versus precision.