Former rental car employee - your head is in the right place but you're missing one thing. Rental car companies (at least the big green one I worked for years ago) don't sell insurance, they sell a damage waiver. All it's doing is waiving their right to go after you in the event of a collision to cover the costs of their vehicle they loaned you.
Why this practice makes sense is let's say they sell X amount of damage waivers per day at $25/day per rental. The average person renting a car isn't going to damage one, so that $25/day is pure profit in 99% of all scenarios. In the event of an accident in the other 1% of scenarios, they simply pay for it and move on. This is of course an insane oversimplification of the process but it's essentially how that works in a nutshell. The process may have changed or there may be new rental damage waivers that do cover personal injury, but I've been out of that scene for awhile so I'm not sure.
So if you're planning on signing up for the rental damage waiver and hoping it covers anything beyond the car the company loaned you - you may be in for a hard lesson. You may have better luck checking what credit card you use to rent, most of the higher end cards offer rental "insurance" in some form or another, again be sure to read the fine print there because no company is going to assume that kind of risk for free.
I'd like to just offer up an edit here as I was replying to user662852 and felt this worthy of sharing with everyone. I dug deeper into the official "coverages" through the big green rental agency I worked for, the wording of these may be newer but the concepts are roughly the same from what I remember. The top level Damage Waiver (DW, or CDW) is as I mentioned above, just the waiver of their rights to come after you if you damage the car.
The second tier is PAI/PEC, Personal Accident Insurance and Personal Effects Coverage which is, "The PEC contained in the policy insures the personal effects of the renter, additional drivers, or any members of the renter's immediate family who permanently resides in the renter's household and who is traveling with the renter against risks of loss or damage." So it covers you and your occupants against injury claims.
The bottom tier is kind of vague but is SLP, Supplemental Liability Protection which states, "If the renter accepts SLP, Enterprise provides third party liability protection up to the applicable minimum financial responsibility limit and Zurich American Insurance Company provides excess third party liability insurance coverage from the applicable minimum financial responsibility limit to $300,000." This I believe is supposed to act as a supplement to your existing insurance policy in the event your claim were to exceed your policy limits. I based my point off this, "Enterprise is not qualified to evaluate the adequacy of the renter's existing coverage; therefore, the renter should examine his or her personal insurance policies or other sources of coverage that may duplicate the coverage provided by SLP."