That is a feature, not a bug. The ideal US immigration system should only welcome extraordinary people into the country.
Low skilled immigrants compete against low skilled workers that are already here and depress their wages. High skilled workers do the same thing but at the top end with the added advantage of generating more tax dollars and GDP (since they have more income).
At its core the question becomes: Is immigration a public policy to benefit those that are here (ie strengthen economy, unify familial bonds) or a charity offered to the rest of the world?
Edit: To be fair - I can see the argument for a supply of immigrant low skill workers potentially keeping wages depressed hitting existing US residents and while it might be good for the wealthy and businesses it might not be good for the majority. I'm in the UK and these arguments are very similar to those covered in the Brexit campaigns and while I voted Remain and I've since come to appreciate more of the arguments on the other side.
Young unskilled workers are a net gain to the economy, especially in an ageing society like the US. It's not charity.
How so?
Having said that, I still think you are on point about the American Dream available for everyone willing to work hard. It just starts before you enter the US since green cards are not handed out that easily even though it is called a lottery.
Your odds of winning are something like 0.2%. If you're one of those selected I believe there's still only a 50% chance you will make it through as they select twice as many 'winners' as they have spots available. I applied for about 8 years I think without success. I then stopped after realising I had nothing to gain from moving to the US.
Also, the program is limited to persons from certain countries (for example if you like in England/Scotland/Wales you cannot apply).