Whether or not contemporary European-style cabinets should have crown molding is largely a matter of personal preference and the overall design aesthetic of the space.
Crown molding is a decorative element that is typically added to the top of cabinetry to add visual interest and elegance to the space. Some people may choose to include crown molding on their contemporary European-style cabinets to add a touch of traditional detail or to complement other design elements in the room.
On the other hand, other might prefer a more minimalistic look and opt to skip the crown molding altogether. Contemporary European style cabinets tend to have a sleek and simple look and feel, thus crown molding might contrast with this design philosophy.
Ultimately, whether or not to include crown molding on contemporary European-style cabinets is a decision that should be based on the specific design goals of the space and the personal preferences of the homeowner or designer.