In a non-POM economy, money can buy only goods and services designated as "luxuries." But luxury is in the eye of the beholder. What seems a necessity to one person is likely to be perceived as a luxury to someone of more reduced circumstances.
Anything can be designated as a "luxury" or as a "necessity" or as a "pink elephant," for that matter. What is important is the consequences of restricting the purchasing power of money to a single category of goods and services. Payers can have no money at all and are not allowed to consume luxuries. Therefore, to label something as a luxury item or service is to deny Payers access to that good or service. Therefore, no good or service which is actually necessary to support life may be labeled a luxury if the system is to succeed.
Also, if people are to desire money and be willing to work to get money, the things which money can buy must be desirable to many people. Therefore, in order to meaningfully be designated a luxury, a good or service must be one whose consumption by a person would give pleasure. This also excludes many goods and services from being treated as luxuries.
But within these very broad limits any commodity or service which may be consumed by people could be designated as a luxury. Therefore those whose task it is to actually choose those items to be designated luxuries will have considerable flexibility and freedom in their choices.
What considerations will lead those who decide to choose one or the other category for specific items and services? I have no way to be certain but I would suspect that this freedom of choice would lead them to use the designations to control the proportion of persons in the society who are Payers. It seems obvious that the more goods and services which are denied to Payers, the fewer people will be willing to make the sacrifice in order to become Payers. Alternatively, the more goods and services which are not really necessary to life which are available to Payers, the higher the proportion of people that will decide to make such a lifetime commitment.
Obviously there will be an optimum proportion of Payers in the population. If there is a very high proportion, each payer will not feel important and will be more likely to be ignored and relatively powerless. Therefore they will not try very hard to do their jobs well. On the other hand, if there is a very small proportion of Payers, they will be overworked and they will not be able to pay for everything that should be paid for. Therefore, the Payers are probably the best organization to decide on what goods and services should be designated as luxuries and which as necessities. That organization will be highly motivated to get it right and keep it right.
Will the designations vary from place to place and change over time? I should think so. After all, goods and services which we take for granted today such as plumbing and electric lights were considered luxuries at one time. I should think there would be similar changes in the future as well. So far as I can tell, there is no reason why such designations should be fixed forever.