Somewhat of a wealth hierarchy is to be expected in any system simply because some people are more fit to make money than others. The only way to "correct" this natural tendency is to commit theft upon those fortunate enough to be more fit to make money. Furthermore, in the case of markets, the only way of acquiring wealth is by satisfying consumer demand.
That said, don't believe that the current wealth stratification we see now is the result of the free market. The free market results in an essentially linear wealth distribution, with an extremely small lower-class due only to their physical inability to work.
There's so much wrong with this *sigh*. It doesn't have to be their inability to work. It could be their inability to find well paid job, because of low mobility, employers monopoly, lack of safety regulations (I'll see you working in death trap of a workplace), over-abundance of workforce in the area... List goes on.
Care to show any examples of monopolies not created by government?
Socialism legalizes the use of force against certain sectors of society, the free market does not.
The question of wealth distribution is a question of practical benefit, not basic morality.
http://www.cracked.com/article_18845_6-secret-monopolies-you-didnt-know-run-world.html
Of course they don't have complete information, but the tendency is certainly toward consumers being careful about where they spend there money.
The market tends towards perfect competition even though perfect competition obviously does not exist.
The law of demand means that consumers tend to take price/quality into consideration.
If something isn't profitable its because there isn't a demand for it.
That is so in perfect market. There are no perfect markets in reality and the closest any given market to monopoly is, the less choice consumers have and price/quality have lesser impact on the decision to buy. Add in the fact the difficulty in entering monopolised branch/industry and you've got mess.
Those difficulties include more experience of the monopolist, more knowledge about market segment, existing distribution networks and "economy of size". Weaker companies tend to merge, get bought or bankrupt.
If they don't, they become strong ones, in which case they tend to merge with those of their size (getting even bigger) or to "eat" the small ones, with the same result. End result is one big ass monopolist (or a few giant oligopolists that might not be in cartel) controlling both the amount of products produced, price of said products and ability of specialised workers to get employed in branch/industry they have educated themselves for (aka ability to decide salary). And even if the big guy allows you to produce some stuff, the fact of the matter is that your price will be higher, your expenses will be higher, the amount you manage to produce won't make a dent in demand and people will still be forced to buy from the big guy in the end, because of that small amount.
And if, by some incredible chance, you survive long enough on the market to be even the smallest threat to the big guy(s), (t)he

can always use dumping prices to win in price war or just simply buy you. And the worse thing, it's natural process and even the perfect market won't stay in perfect equilibrium for long and will become imperfect.
How is a street light not profitable?
How do you think it could be? .
It takes too much effort to build the infrastructure, it is extremely hard to know who is using the service, it is even harder to make people pay for using it and there's no efficient way to cut people refusing to pay without cutting lots of "paying customers". So? Any ideas to make it profitable?
If something isn't profitable its because there isn't a demand for it.
Demand is not the issue. Supplying it is the tricky part, if you do it for profit, because costs outweigh profits. But, if you are state and are doing it because you want to lower crime rate and the number of accidents happening in the dark... Well, it's completely another ballgame.
Or, if you don't like that example, take another type of goods and services. Those that are beneficial for the society as a whole but usually don't turn out profit. Water recycling, for example. Is there a huge profit margin in taking a raw sewage, turning it into clean water and returning said water back into the river that I am not aware of? Mine sweeping. Disaster relief.
My point is, people have more motivations than greed (profit!) alone. Compassion. Lust. Desire for respect. Hunger for knowledge etc.
Private charity must also be considered, which would be greatly increased if it wasn't so deincentivized by the state.
What you theorise about (free, unregulated market) was tried once. But it was tried extensively, for a few hundred years. It didn't work then. It was changed into the (better but still not perfect) system we have now. Tell me, why should we get back to something that didn't work?
The rich had no reasons to give to the poor then and never gave enough. The main reason to give usually boiled to "If too much people starve to death or are hungry enough, they'll get angry, pick their scythes and hammers up and raise against us."