From the other side, I used to have a few privately owned aircraft on line. I'll be tactful here and say the the biggest problem was the "unrealistic expectations" of the owners, no matter what was written into the contract. Very few of them understood the realities of owning an aircraft and some even tried to undercut me by doing sly deals on the side with my hirers. So apart from the opportunity cost mentioned above, don't expect every flying school that has its own fleet to want a privately owned one on line.