Just one thought on the whole range of money vs. fairly consistent level of money.
Let's say I own a large bakery that specializes in your basic breads (nothing fancy, so the elites of society aren't attracted.) Right now my target consumers have incomes between $10,000 and $50,000 per year, and I'm selling my bread at $1 per loaf. Now to make this more interesting, lets say that the vast majority of my consumers fall into the lower half of that income scale, between $10k and $25k. Also note that the employees I keep at the bakery are making $25-$30k a year (right around the average income of my target group.) Certainly bread is important and at $1 a loaf even those making just $10k a year can afford my bread.
Now let's change the economic system and balance the incomes, taking the same group of consumers but now letting their salary range be from $30,000-$50,000, with the average falling right in the middle. What this translates to is that the same consumer I was marketing my $1 a loaf bread to now has 2-3 times the amount of money in their pocket, plus my costs (due to wages and such) have also gone up. To make the same profit on my loaf of bread I may have to charge $3 a loaf.
Here comes the real question, what is the difference between a person making $20,000 a year and buying bread for $1 a loaf, and a person making $35,000 a year and buying bread at $3 a loaf? The person making $20,000 can buy more bread.
Yes, this is a simplified example as it doesn't take into account food stamps or other government subsidizing, but it also shows what would most likely happen if there was some large push to even out the incomes. The higher the average and the minimums go, the higher company costs go, and the more they feel they can charge for their product because there is more money going around.
What I'm not saying here is that we should make sure people are always stuck in a state of poverty, what I am saying is that a simple money redistribution program is not the answer.
Now more directly to your question of why people face money problems.
What motivates a rich man to work harder? The idea that he can become richer.
What motivates a man getting a free lunch to work harder? Self respect is about the best reason.
If we take away the ability for the rich to get richer, they might as well close down their businesses and send all their employees out on the streets.
If we hand over money to balance incomes to those that "need" it, we undermine those that are trying to work for it, although you might influence a few that don't want to be classified as "needy."
But then one must wonder, if those people don't want to be needy, would they be working hard trying to raise their status normally? The answer here is probably yes, they would already be working their butt off, even without a label.
So what have we gained by trying to balance the economic situation? Businesses have shut down putting more workers in the unemployment lines, more people have been convinced that the free lunch plan is the way to go, and the same amount of people are still working trying to better themselves.
That wide range of rich/poor gives people motivation. Its good to know that someday if you work hard (or even if you're just plain lucky) you could be vastly more wealthy than you are right now. There is no "easy" way for this to happen, it takes hard work, and there are too many people looking for the quick solution (i.e. lawsuits, lotteries, etc.) Simply raising the minimum/average wouldn't work (see bread example above) and capping the wealthy doesn't help anyone.
I've seen the poor or "under-priviledged" work hard and succeed, I've witnessed that when a man buckles down, works harder (and I mean hard, not just put your 40 hours in and forget about it, overtimer, off the clock, read a book you don't have to hard. I have a brother that was putting in 80-100 hour work weeks to provide for his family, the proudest moment of his life was when he finally could stop doing that and say "I made it," and I have more respect for him than most people in this world. He didn't graduate high school either, but now works with equipment worth hundreds of thousands, owns his own home, has two kids, and all that too.) than the norm, they can make it. It isn't about the level of eduction you receive, its about what you can do with the education you have. Those that don't even graduate high school can still make it, but it takes another level of dedication, the wanting to better themselves.
The only man that traps someone into a life of eternal poverty is that man. Opportunities might not come as easily for everyone, but if they work their tail off, they can get themselves that opportunity.