Every person who does a job in this country "serves", and many of them receive very little for their service, however vital that service may be - for example care workers.
Members of the royal family do perform certain functions but I don't think those functions can be compared to that of ordinary working people. Meeting people and shaking hands with them for a couple of hours a day cannot be compared to, for instance, doing a long shift in a hospital, making your own way home and being responsible, after a full day's work, for all the domestic duties that arise.
The royal family lives a very cossetted existence, with all the extraneous duties that ordinary people have to perform, taken care of by someone else. Yet it is those ordinary people who pay for the upkeep of this family.