I haven't had many opportunities to put myself at risk of liability, and I can see why this can be a concern if your vulnerable asset is your airplane or your business, but ...
If you ask the question "which benefits aviaton more in terms of public image and real safety- skilland knowledge, and trust in them, or insurance policies?" the answer is pretty obvious.
No piece of paper is going to keep me or my pax safe. To paraphrase Richard Bach,
I am your insurance policy. The insurance company isn't flying the plane, nor does paying X amount per year make me a better pilot. And no amount of money is going to replace a life or a limb.
I carry non-owner's insurance, mostly for renting, but if I had a potential pax who was going to base their decision whether or not to fly with me on whether or not they were covered, I'd remind them of that. I might even decide I don't want them to fly with me.
Nobody's asked yet, and I don't ask when I'm going for a ride. I might ask about the pilot, the airplane, and the planned flight, but I don't ask about the insurance. Nobody's asked me when they've offered me the controls of their airplane, even one they know I am not familiar with.
That being said, I don't have a lot to lose, asset-wise, so I dn't expect those who've been at the pointy end of a lawsuit to give a damn about my opinion.
This question also reminds me of what an older, independent CFI once told me: he's not insured as an instructor because he feels that "they will not come after you if you don't have anything". I guess in his mind, the cost of maintaining the coverage, plus the effect on his premium if he is ever held at fault in an accident but the insurance company provides the deep pockets, isnot worth what it provides, which is, basically nothing in terms of his own ability to keep his flights safe.
This makes sense to me on the surface, but perhaps nowadays that is no longer the case, with the "shotgun" approach...?