I'm not sure if you're expecting to get a reply that encapsulates all of HN's users position on this, but probably the reason that you see more H1B talk here is because this site caters to people in the tech industry - affected by H1B's more than the industries that are more affected by illegal immigrants from Mexico.
No I don't advocate anarchy, I advocate we enforce our border as any state does, in fact its one of the few things I actually think the state is suppose to do. If we cut out just a small fraction of all the stuff the state does which I do not think it is suppose to do this job would be done, and done well and would allow only higher quality individuals into our cities and communities (e.g. not drug dealers and criminals).
>The population of illegal immigrants is many time higher than the population of H1Bs.
Why does this quantity matter in the context of H1Bs, you are confusing two different issues. In one case the law is not enforced, that clearly just needs to be dealt with. H1Bs on the other hand is a legal system which requires refinement at the legislative level, or litigation.
The other involves illegal border crossings by individuals from a neighboring country or visa-overstaying mostly from South America.
I've personally witnessed a kind of overlap of these problems that went way beyond H1-B fraud and went way into human trafficking and organized crime. In that case a high-tech company was being used as a front for illegal immigration from an Asian country, with no-show workers and other amazing stunts more typical of a corrupt government or union operation. But that was an exceptional case.