A licensed aerodrome (Art 101) is required for training to become qualified for the grant of a pilots licence or the inclusion of an aircraft rating, night rating or night qualification.
A licenced aerodrome is not essential for IMC training, FI training, IR training or the revalidation or renewal of a rating in an existing licence.
As already said, the instructor is the one putting his licence on the line so it is his responsibility to exercise a duty of care, especially in these days of civil litigation. The purpose of authorising solo flight is for solo consolidation to take place following dual training, not to allow unlicensed pilots to break the law (Art 21)