Based on practice and customary international law, the criteria are there. It is totally available for the government to make an assessment based on those criteria.
It could also look into other elements that it wants to take into consideration. It's not an exhaustive list. As I mentioned in my preliminary statement, there could be factual situations that warrant additional elements being added into the mix, such as political considerations or an analysis of where the entity that seeks to become a state, under those criteria, is in relations with its neighbours and the region.
These are additional elements, but I wouldn't see them qualifying as impediments.