John
However, for real world situations, the load on the nosewheel is a small fraction of the aircraft's gross weight so a small change in load should result in a much smaller change in tyre/surface coefficient which, I suspect, will tend to get lost a bit in the face of other, larger forces
The tyre/surface coefficient won't change appreciably, but the ability to resist yaw is coefficient times NW reaction, and a change in nosewheel load from (say) 4% to 6% TOM is a big increase in NW yawing moment potential even though both are relatively small fractions of gross weight.There has to be a reason for recommending forward stick during TO run.