Honest question: What would be the liability risk proposed to be covered?
We'll presume that the aircraft itself is properly insured, so anything which happens as a direct result of that training flight is covered.
Thereafter, pre license for the student, the instructor is PIC, and any liability path is through the aircraft insurance.
Once the student is licensed, should there ever be an obscure claim of liability relating to the skill (or presumably absence thereof) of the student now pilot, would that not disappear in the reality that that pilot had obtained a license to act as flight crew, and thereby met a national standard for the skill? I think that if the student/pilot had met the skill requirements, there would be no lingering liability for the instructor, who obvioulsy had taught the lessons adequately.