You are severely underestimating the importance of peace of mind. When you are poor, you are always worried about making rent. When you are middle class, you might be a few paychecks (or a hospital bill) away from insolvency. The wealthy don't have to worry about those things.
John Scalzi has an awesome post about the cost of being poor[1] on his blog.
http://whatever.scalzi.com/2005/09/03/being-poor/
Edit: d'oh, my reply is off-topic because I misread GP's post - missed that the distinction is between 1%ers and 0.1%ers. Considering that; I suspect the difference is in influence (my guess is the 0.1% are likely to be more 'politically involved' or better connected)
See https://en.m.wikipedia.org/wiki/Alice_Walton#Automobile_inci...
As others have said, even most of the top 1% isn't immune. They have to work to make money. Many people who are not billionaires probably spend more than they earn making them vulnerable to losing almost everything if they have to spend a year or two in prison.
Why will they be killed by the police? Are they threatening someone or do they look like they will?
All of the things you listed come down to attitude and personal choice.
In many places in the U.S. "look like they will" is synonymous with "having dark skin". What a horrible attitude and personal choices these people must have.
If you think in term of investment opportunities, clearly there are many investments that are only accessible to wealthy people, because of the amount of risk they involve, or because owning a tiny fractional share of a company is a sort of anomaly. Most investments (building, company, project) have few and require few investors, not the least to ensure proper governance.
But at one point the marginal benefit of the accumulation of wealth becomes zero. I don't think someone who own 1 billions lives much better than someone who owns 50 millions.