A cosmetic product may be placed on the European Union market only where a legal or natural person established in the Union is designated as its responsible person, and for an imported product that person is the importer by default unless it designates someone else in the Union by written mandate accepted in writing.
A brand shipping into the EU from outside cannot be the responsible person itself, so the question is not whether to appoint one but whether its distributor becomes one by default and inherits the legal exposure along with the shelf space.