The system truly isn't equal. And from outside is bit bizare.
The US has 50m foreign-born residents, the second highest is Germany at 16m. There's no country on Earth which takes in more immigrants (I'm actually one of them!) yet my whole life I've seen nothing but people demanding that they take in even more.
1. If you want equality then apply it to H1B itself. Why is it that you want equality when it comes to green cards that give people equal rights, but not when you want to bring them in to do work? Apply country caps for H1B visa and let’s see how that works. Equality for employment green cards but not for visas is not a system of equality.
2. Apply equality everywhere else as well, family immigration especially.
3. You could design a system that is more equal if you really wanted. You are quick to blame huge populations, but also ignore the fact that countries like India and China are almost as big as Europe. Take into account the size as well if you wanted equal representation.
Defining fair is not easy, but you can at least try.
On the other hand, children of undocumented immigrants get citizenship without any quota. So there are many more new citizens from Mexico and Central America vs Europe. I am not saying they are bad citizens, but there is some rational limit to immigration that protects native culture from sudden disruption against wishes of existing citizens. So, defining what is fair is not as easy as you might think.