I think that we should have both state cemeteries and private ones.
State cemeteries should be kept at the expense of the budget and provide a minimum level of services free of charge (plot of land for the grave, security and cleaning of the cemetery territory). In the state cemetery, competing with private companies, should be given the right to provide additional services at the request of customers (digging a grave, erecting a gravestone, burial procedure, etc.) for an additional fee.
Private cemeteries in its territory can provide various services, from a plot of land to the erection of tombs and a funeral service.
Thus, rich citizens should be able to bury relatives with pomp and in expensive way, but low-income citizens should be able, at least, to bury their family member free of charge in the state cemetery.