I understand that anyone's question of "how much insurance should I carry?" is met with an answer of "it depends.." My question is: depends on what? What parameters do I use to determine what is right for my situation?
You can't eliminate the risk and exposure - if you crash into a schoolyard and paralyze 6 kids, you WILL get hit with a suit for more than any insurer would cover, and if you lose, you WILL be on the hook forever, since in some states you can't get out of those obligations through bankruptcy. Of course, the same thing could happen in your car.
So let's leave out the extreme case - since you can't do anything about it other than NOT crashing, which you're already planning on.
Let's take a more realistic case - you're a little off your game and you damage the airplane. Now you owe somebody for the damage. The damage could be as simple as a blown tire and a new wheel pant for about $1500.00. It could be rebuilding/reskinning a wing panel for $5000-20000. It could be a new prop and engine for $45,000.00, or it could be a replacement airplane.
So that's the amount of money you COULD be asked to provide. If you've got a house and college savings and other assets to protect, then you can then pay a premium (lay a bet) with an insurance company for coverage. If you're super-rich, you could just self-insure and take the hit (but then why don't you OWN your own airplane?). If you've got no assets at all, then you might plan on declaring bankruptcy in the event of a judgement, and I believe that in SOME states you can do this if personal injury liability isn't involved.
The bottom line is that a responsible person looks at the potential threats to his wealth and takes measures to protect it. Renter's insurance is one way to do it.
I've flown "naked" as a renter back when I had few assets. Now with the house and the wife and the child (and other toys), I cover myself, either by only flying airplanes where there's a contract in place that limits my liability (when I ferry airplanes), or as a named insured on a policy (when I ferry or teach), or by providing my own coverage, at least for liability.
IF you rent from an FBO that has a no-subrogation policy, where your responsibility for aircraft damage is contractually limited, then I'd recommend you get a liability policy for whatever value you think is reasonable, to cover you in case a passenger is injured or you hit Farmer Bob's best heifer. If you don't have that aircraft damage covered through your contract with the FBO, then you should get your own hull coverage.
I hope this was helpful - you've given me a good idea for an article. Now I just need to find the time to write it.