Reversibility = non-causality. Can this be right?
You're right as far as it goes -- if you can come up with a Newtonian system that reaches a stationary state from a non-stationary one, then the system must be non-deterministic.
The point (to the extent there is a point here) is that this is not as easy as you seem to assume it is. The vast majority of nice smooth Newtonian systems cannot reach any stationary state, save for having been in it forever.
The value of Norton's Dome as a thought experiment is to provide a proof that there are Newtonian systems that can reach a stationary state at all. If you can define another system with this property, it will be just as good as the dome for making whichever point you would otherwise use the dome to make.
The (slight) controversy that appears to exist around Norton's Dome is not whether the conclusion the thought experiment reaches is correct, but whether it is an interesting conclusion to arrive at at all.
The pragmatic counterargument goes something like: Yes, yes, a precisely defined Newtonian system is not necessarily deterministic, but why should we care about that? We know our world doesn't function precisely along Newtonian lines anyway, so a shortcoming of the mathematical formulation of Newtonian mechanics which requires infinite precision and therefore -- even before we consider quantum effects -- is impossible to manufacture in practice ought not to keep us up at night. It would be much nicer to know, for example, whether your favorite quantum field theory is mathematically consistent!
As a counterpoint to this, Norton's Dome serves as a relatively simple didactic counterexample to the popular conception that "classical mechanics was nice and deterministic, but with quantum theory we suddenly have to grapple philosophically with nondeterminism. Oh, woe is us!" The dome example shows that the Newtonian picture does not necessarily give us determinism -- and actually it can give a kind of nondeterminism that is far worse than what quantum theory does, in that it doesn't even provide us with any principled way to assign probabilities to when a resting mass at the apex will start to slide down the dome.