I have been studying on Skype for several years with one teacher, and with that teacher's permission, branched off to side-studies with a second teacher who has his own specialized angle. Musiclessonsanywhere, on your site you say that in-studio lessons and on-line lessons are the same - I would say that they are not. Each has its advantages and disadvantages.
Good lessons will include the physical component; how the student sits, moves, uses the hands etc. If natural, you leave it alone and maybe tweak it over time. Simply trying to produce the right sounds, the music, if the physical part isn't working, is frustrating. This is the weak spot in on-line lessons, and something we have worked to overcome. We have two sets of cameras to content with --- that of the teacher, and that of the student. In live lessons the teacher can walk around the student, and can also touch a shoulder and say "relax this area". We sorely miss this in on-line lessons.
That said, on another instrument I got into technical trouble because the teacher was not that observant, and on piano, my on-line lessons are actually more effective even for the physical, than the in-studio lessons had been.
On-line does not need to limit itself to the interaction on Skype. Do you save the videos of the interaction, so that your student can study and rewind the lesson to get more out of it? (In-studio some teachers now tape the lesson, or the student does) for the same purpose. Some on-line teachers create teaching videos on particular subjects, which all students can work with. So a careful lesson is crafted, which can be used from then on by everyone. Students can also video their playing, send that to the teacher (private Youtube channel for example), for the teacher to study and give feedback on, or to address in the next lesson.
Do you do any of these things?
If in your joint project a teacher responding to your offer were to have other methods such as what I outlined - or if they focused on additional or different things - how would that work out?