>>> A poor person has to buy insurance for his house and car,
We're doing pretty good here if a poor person is implied to have a house worth insuring (implying either ownership or rental of sufficient value, containing sufficient assets) and a car, and is eligible for bank loans for both. In some countries, a person rich enough to have a house, a car and to qualify for bank loans for both is considered pretty well-to-do.
>>> A rich person can buy things in cash, and then self-insure using his assets to cover accidental losses.
I'm pretty sure most people, not only poor people, use car insurance. It's more convenient and usually (unless you drive exotic or super-expensive cars) cheaper than surety bonds that are usually required, and same with cash deposits (since cash deposited at DMV can't be used for anything else). For businesses having massive fleets, OTOH, it may make sense to self-insure since they get the same risk distribution as insurers, but without the middleman.
>>> overall, being poor is a very bad business policy
It's bad business, but you may have a lot of incentives for it, given that welfare subsidies and services you may get in many US localities pay more than minimum wage job and in some localities more than average wage job.
http://www.cato.org/publications/commentary/why-get-welfare
http://www.cato.org/publications/white-paper/work-versus-wel...
>>> rich getting richer and the poor getting poorer is backed up by simple economics.
It may be but it definitely is not backed up but what you said. The thing is that statistics that talk about "rich getting richer" makes you assume that same people that were rich 20 years ago got even richer now, and same people that were poor 20 years ago are even poorer now. In fact, nothing in this statistics point to it - what statistics can tell you is that some people were rich 20 years ago, and some different people are rich now, but it usually says nothing about how many of people rich today were rich or poor 20 years ago. It is completely normal for a person to be piss-poor while being a young student and become quite well established when retiring. Usually it comes from working hard and making a number of right choices on the way. Including, yes, saving diligently and having long-term view, which leverages the power of compound interest - but for this you need the right behavior.