Graduate Key problems in classical and quantum measurement

[A. Neumaier]

The well known problem of classical stability of the atom would apply.

Only if you model atoms as composite. But one can model atoms as point particles with effective interactions.

Its probably much easier to do if you work with hard potentials

Yes, but then it is not microscopic. The challenge in solving the quantum mechanical measurement problem also goes away if you don't model the detectors as multiparticle systems. Nothing worth doing remains once you take an apparatus as a black box with simplified laws - whether exact reflection classically or some form of collapse quantum mechanically. The foundational challenge is to show how these assumptions are compatible with an underlying microscopic dynamical law. The work by Allahverdyan, Balian and Nieuwenhuizen is relevant only if one is interested in taking up this challenge.

You can always construct a domino like effect, with a ball on top of a potential rolling down knocking out other which are heavier etc.

There are indeed papers that address this quantum mechanically, using multiparticle models. Doing the same with classical multiparticle models is an interesting challenge.