Plus, i read somewhere that the amount of successful American companies founded by immigrants is just crazy (although they probably didn't all get through with the H1B, of course).
Take my case: i got interested in the American market early in my career, when i realized people found me good at what i do. I'm very interested with innovation, and France is known not to be the right country to achieve that. I proceeded to try to find a H1B, to no avail: i needed an employer who wished to pay loads of money to hire me, and i didn't have a good network for that. Plus, even if i had one, we were off quotas until the following year, no one could get a H1B for almost a year.
I met an American guy who was interested in my application. I wasn't so expensive, this was early career. But he just couldn't afford to pay for all the surrounding fees, it was just easier for him to recruit in the US for now.
Unlike what you're pretending, i didn't chase the unchaseable, and started working in my home country for a few years (i'm from France). I figured, if that country doesn't want me, well, i'll be happy wherever.
Fast forward to 5 years later: in the meantime, i spoke at a lot of conferences, i wrote a lot of articles, and i'm publishing a book for the biggest IT publisher in France. An immigration lawyer from New York told me this made me eligible for another kind of visa, not based on my skills but on my accomplishments: the O-1 visa.
Problem: you still need an employer for that, who is willing to pay a lot of money (albeit less, i believe). I learned a bit about regulations in Canada, and elected to rather go there: the permanent residency (just like the American Green Card) is just a matter of patience when you have the right credentials (and not such a crazy patience: it's 12 months when you're French, and you're good for a lifetime).
Within the six months i needed to build the case, it turned out i met a French employer who was looking for someone with experience in conference speaking, article writing, and in product marketing, to carry their effort to the US, where they are way more famous than in France (i'm not yet at liberty to disclose who it is, but let me tell you, this is a once-in-a-lifetime kind of position). We're starting to work on the (crazy dense) O-1 file that we'll turn in, and i'm glad i don't have to pay for that anymore!
And this is how i end up on this forum! :)
Lesson to learn: during these five years, i brought a lot to the French web community, which gave a lot to me as well. If it had been easier for gifted people to get to the US, i would have done all this work in the US, for five years.
Also: when i'm in the US, i'll submit an EB-1 request, to possibly get a Green Card and get the matter sorted (this is still based on my achievements). If i get it, i'll gladly stay for a large chunk of my life, and try to do as much good there than i did in France. If i don't get it, no big deal: i'll finish the file i had started preparing for Canada, and i'll go there. I like to think i go where the wind carries me, and my skills are requested. I won't be mad at the US if they decide they don't want me longer, but i won't cling to it like you say, because i don't really need to. I'm ready to do great things where people want me.
This is my experience with H1B and American visas, so you'll understand i don't really see myself as someone who would sell my soul to get a Green Card, and who would agree to be underpaid, at all!
I could tell you a few similar stories from other French people who meet the same difficulties. When they say the American immigration system is broken, well... there are many way in which they are right!
People with the opposite approach, i'd be glad to hear about your stories with H1B.