Shy .... as we all know ANY flight can be a “ private” flight !! In fact there is almost no need for anyone to have an aoc other than for random ad hoc charters .
Most people that charter do so more than once so are perfectly able to buy a block of hours and do all their flights as private flights and thereby opening up the ability to fly into Battersea for instance in a non float equipped single . I don’t know any operator who specifically does not want to have an aoc .... they just find it impossible to operate as a small company, maybe with one aircraft, with one !!! My prediction years ago of no small companies having their single on an aoc has almost arrived. I’m going to give it another go , having tried before , but I am not hopeful as 90% of my business is likely to be lease .
The future for most pilots I know is all freelance and not on aoc .