The problem here is that the insurance rubric is really not all that valid in the real world.
In the real world, if you get sued because someone gets badly hurt (or worse, killed) and its your fault (and sometimes even if its not really your fault!), all the insurance you can afford to buy won't do you a damn bit of good. Awards for that kind of thing are not measured in the hundreds of thousands of dollars, but rather often in the tens of millions, especially if the person who buys it is relatively young, has a family, has a six-figure job. Do the math; the lawyers do.
Consider that a young 'thang down here in Destin was just awarded something like three quarters of a million bucks - because she took her clothes off in front of an open window in her condo and some security guards watched with a pair of binoculars. She put on an exhibition of her body and got paid because some lecherous men saw her, through a window where SHE left the curtains open, and looked!
Now consider the guy who is making $100k a year, has two young kids and a wife, lives in a $300,000 house, is 30, on an executive "fast track" with a college degree and dies because your reg service sucked. You think that a million or two worth of insurance is going to do anything for you? You're smoking something.
That is why you incorporate.
It is why, if you are doing something risky, you incorporate more than once, and the risky things are partitioned away from the other stuff you do.
It is why, if necessary, you put all your personal assets in trust and basically make yourself "poor", just in case someone manages to pierce the corporate veil.
And you do all of this with expert legal advice so that in the event the smelly brown stuff hits the airmover you don't wind up in the poorhouse and lose everything - including your shirt.
Now once you do this, then this argument about indemnifying through some insurance company becomes pointless. Oh sure, you still have insurance. You need it, among other things, in case an ordinary disaster (as opposed to an extraordinary one) happens. Your building might burn down, a tornado might visit your town, someone may burgle your place of business some night, etc.
THAT is the purpose of insurance - protecting against things that would wipe you out as a business, but are quantifyable risks with quantifyable dollar amounts of harm.
Trying to protect against open-ended liability suits with insurance is a nice dream, and insurance salesmen will try to tell you they can handle it, but the truth is that they can't and won't. They won't write the limits and terms you really NEED to have slam-dunk protection, at least not for a premium amount you can afford. Only Lloyds handles those kinds of numbers, they don't do it for amounts you can afford to pay as a small business owner, and even they have some nice weasel-words in their policies - just enough to keep you awake at night.
Never mind that in a worst-case scenario the insurance company can actually cost you. How? In return for that insurance you give up the right to manage your own defense if you get sued, at least until the limits of insurance run out. Why is this important? Because if their limit of liability runs out you're already committed to their mode and method of defense and they walk away at that point - which might be completely different than how you would have done it. After all, they might have intended to try to settle for significantly less than your full liability limit - you, on the other hand, would probably prefer not to pay anything, especially if you think you're right.
My position on insurance when I ran my company was that its primary purpose was to cover ordinary business risks. While we had liability insurance (and there were plenty of ways to get killed or seriously injured in our shop and on the job!) keeping the firm and me personally safe from those risks wasn't the primary purpose of my insurance - that job was really one for proper corporate organization.
Anyway, I've said this before, and I don't expect to convince anyone who doesn't believe me. But I will argue that those who run a business and don't understand this need to spend a couple of hours with a GOOD corporate attorney - before they find out the hard way.