Yeah, if you've got a loan, I bet going uninsured isn't an option.
I'll be paying cash for my first plane but still want insurance. The way I make that decision is simple. I just ask myself a question: "How much will it hurt if I wreck the plane and write it off?" In my case, losing a $40,000 or $50,000 airplane would be pretty painful. Not the end of the world financially, but I'd be really upset about it.
For some people, losing an airplane is no big deal. They've got enough in the bank that it wouldn't even register emotionally for them, so they can self-insure if they want. If I were in that position, I'd still want a good liability policy because big-time wealth is like a giant target on your back for lawsuits.
So if you'd miss the money, pay for insurance. If you wouldn't, you can go without. It's kinda ironic, but that's life.
My insurance is only going to be $694/year for a Cherokee 180 with a hull value of $50,000. That can factor into it, too. The higher the premium gets vs. the value of the plane, the more sense it makes to self-insure.