The keys here is both that Bankruptcy is a thing, and you are going to fight much, much harder against a suit that goes after your assets than one that goes after your insurance coverage.
The distribution of accidents is going to be very non linear. Some cases are going to be 1000$, some 10000$, some 100000$, some 1 million$ and some 10 million dollars. And some even larger.
Carrying enough insurance to handle a 100 million dollar accident when you are worth 1000$ is a waste of money. Simply going bankrupt if and when it happens is cheaper than the cost to carry that policy. You lose 1000$.
If you are worth 100 million dollars, the same policy and accident costs you your entire 100 million dollars, minus the amount you are insured. Here, there is increased benefit to you from the higher insurance values; meanwhile, for the person with 1000$ net worth, all insurance short of 99,999,000$ doesn't matter. You go bankrupt regardless.
The same holds at every level.
The next is the fact that people might decide to sue or settle for an amount based on your insurance coverage, if the benefit of going over is limited.
If you have a 100,000$ policy and 1000$ net worth, asking for more than 100,000$ isn't going to benefit the person bringing the lawsuit much. Even if there was an 1 million dollar accident, why not settle for 100,000$ if it can get the other witness (you) on side.
If you are worth 10 million dollars, putting that full 1 million dollar lawsuit through becomes a lot more tempting.
When your coverage is roughly equal to your net worth, people settling for half as much as they could get in exchange for you being a cooperative witness to the settlement becomes tempting. When your coverage is much smaller than your net worth, it becomes more tempting to fight it out.
So, lets look at Alice and Bob. They get in a 500$ accident. No difference.
They get in 5,000$ accident. Again, no difference.
They get in a 50,000$ accident. No difference.
They get in a 100,000$ accident. In Alice's case, the cost is only on her insurance. In Bob's case, it will wipe him out. Who do you think will fight harder against the lawsuit, and who might be more tempted to be a cooperative witness in the lawsuit?
Next, they get in a 250,000$ accident. You can't get blood from a stone; if Bob offers to settle for 50,000$, they have to choose between a potential 100,000$ payoff or a 50,000$ payout without a fight. If the costs of the lawsuit plus chance of winning is 50% of the payout, you take it.
In Alice's case, the calculus of the other side is 50,000$ payout or a potential 250,000$. It looks a lot more tempting to not settle. The costs and risks of not settling can be 4x higher and still be worth it.
Going bankrupt isn't the end, and what liability insurance protects is your net worth (well, and your garnished earnings while bankrupt; you can factor that into a pseudo-net-worth). If you have no net worth, you have nothing to lose from your liability. If you are worth a lot, then you have lots to lose from liability.