Bullets that are hard to start seem likely to provide poor accuracy due to the likelihood of misalignment with the barrel and deformation of the soft lead bullet. In watching Idaho Lewis videos on loading ML's, bullet casting, accuracy tests, and so forth, I've noticed that he uses bullets that almost slip down the barrel under their own weight. Not good for hunting due to the likelihood that they will move off the powder charge... but even for hunting, I think you want bullets that fit so well that they can be started by hand, and pushed down to the powder with relatively little force.
Modified Minie bullets which have under-diameter bases with small hollows, like the Hornady Great Plains and PA conical, are easier to start straight, and upon firing their bases expand to engage the rifling, so they stay straight as they travel down the barrel. That may be why they have a reputation for accuracy. More conventional Minie bullets with big hollows in their bases, like those used during the Civil War, have centers of mass that are far forward in the bullet - far enough to be ahead of their aerodynamic centers of pressure - which also gives them a measure of built-in aerodynamic stability.