Interesting question. I think the truth both practically and principally, lies somewhere between your points 1 and 2.

No matter the size of the cell, if we use PBC we enforce a quasi-periodicity on the system, which numerically may be hard to converge (the self-consistent loop) with too few k-points. So in practice you might want something like 3x3x3 because of that, even if yes, if the cell was large enough, 1x1x1 should be enough. The problem might however be that "large enough" may be too large for DFT...

On the other hand, if by converge you mean "minimize the total energy as function of k-point sampling", I would actually stick to 1x1x1 since there are other approximations in DFT that may be larger. Energy convergence in k-point sampling is notoriously slow and typically even oscillates, and for special systems even depends whether or not you include "magical numbers" like multiples of 3 in the case of graphene (ok, this is not so relevant for amorphous systems with no symmetries).

So, in summary, I would use the largest possible cell from a practical perspective, and stick to 1x1x1, unless there is convergence issues in the SCF loop.