you contrasted "spontaneous" with "closed,"

My point was that true randomness of any kind would be evidence that a system is not closed. This might be a novel observation (I haven't heard it before) but I think it is a logical one. It is relevant to reductionism (we wouldn't want supernatural processes swooping down to make choices for our free processes) and whether we are in a simulation.

Spontaneous symmetry breaking is part of stat mech. [...] Stat mech can be interpreted probabilistically, but it is not at all controversial to apply it to deterministic systems.

When applied to deterministic systems, the spontaneous symmetry breaking isn't really spontaneous, just apparently so. The idea is that the direction of breaking is determined by the initial conditions, but we may not have enough information about the initial conditions to predict it.

Spontaneous symmetry breaking is part of stat mech. It has practically nothing to do with QM.

It sounds like you want like to argue with whoever is responsible for, "spontaneous symmetry breaking in subatomic physics". I didn't mention QM apart from that.