Yes, this "inertia-of-force" is not part of Newton's laws, but it's a straightforward extension of Newton's laws, not a contradiction. And it preserves all of t

Yes, this "inertia-of-force" is not part of Newton's laws, but it's a straightforward extension of Newton's laws, not a contradiction. And it preserves all of the other interesting properties - energy conservation, time symmetry, determinism. It's certainly less of a contradiction of Netwon's laws than the idea that the particle just sitting there can suddenly start moving, which is a straightforward contradiction of Netwon's first law, and implies that a particle can acquire higher order acceleration (jerk or snap) out of thin air. Of course, this is all moot anyway, as this type of dome with a point-like apex is not a physical system to begin with: since matter is made of atoms, it can't have this type of singular point. Not even going into problems of the precision needed to give the particle just the right initial speed to actually have exactly 0 velocity at the top.