Of course the Basic Regulation can be changed. But not by EASA - it would require EC political will and effort:
Such measures shall also include provisions for the issuance of all types of pilot licences and ratings required under the Chicago Convention, and of a leisure pilot licence covering noncommercial activities involving aircraft with a maximum certificated take off mass of 2000kg or less and which do not meet any of the criteria referred to in Article 3(j).
Just delete the part in blue, then 'devolve' competence for sub-ICAO licensing to national authorities under the principle of 'subsidiarity' which €urocrats are always quacking about!