I don't think the purpose of the art collection is "to serve King Willem-Alexander or the future Queen Catharina-Amalia". Instead, to use the same terminology that is used in the UK to refer to the Royal Collection and the Occupied Palaces Estate, they are "held in trust by the sovereign for the nation".
No. The nation has nothing to do with it. The foundations were set up by Queen Juliana, essentially her inheritance went to a fifth, non-natural legal entity, aside her four daughters. It has nothing to do with the nation. The descriptions of the royal foundations are clear:
The Foundation Archives of the House Orange-Nassau 1968:
"To collect and to manage the archivalia of the House Orange-Nassau, the House Nassau, or a House related to these"
Manager of the Foundation: His Majesty The King
This foundation is the base of the House Archives and it's building in the park of Noordeinde Palace.
The Foundation Regalia of the House Orange-Nassau 1963
The Foundation Crown Properties of the House Orange-Nassau 1968
Both Foundations merged into the Foundation Crown Properties of the House Orange-Nassau 2008:
"To ensure that descendants of Her Majesty Queen Wilhelmina, princess of Orange-Nassau, have properties at their disposal, needed for the execution of the royal dignity"
Manager of the Foundation: His Majesty The King
This foundation is the base of the countless properties in the palaces which are in use. From carriages to jewels. From artworks to goldware.
Foundation Historic Collections of the House Orange-Nassau 1972
"To collect and to manage works of art and objects related to the House Orange-Nassau or the House Nassau which are no longer in daily use"
Manager of the Foundation: Her Majesty Queen Máxima
This foundation is the base of the countless objects loaned to exhibitions, loans to Het Loo Palace, loans to museums in- and outside the Netherlands, loans to private houses of members of the royal family.
Sotheby's stated that the offered items (drawings, china, glassware by Lalique, some 18th C silverware) are "property of a Dutch princess". The drawing of Peter Paul Rubens was acquired by King Willem II, the Lalique glassware a gigt to Queen Juliana, so we know it is from the inheritance of Queen Juliana to one of her daughters. It seems the drawing was seen in the New York appartment of Princess Christina, so possibly she is the seller.