This is unfortunately still the case. H1B lottery is still a thing. I had to lose a team member and the person saw a similar email in their inbox. Sucks!
The lottery is still a thing, but I vaguely recall that a few years ago they slapped down some of the foreign outsourcing companies that were abusing the system. I'm I remembering correctly?
H1B has a global cap, so there's a lottery. It's a completely different thing.
Green Cards also have a cap. China (and India in particular) are screwed. If you are from India and take your 1 year old baby to the US, it's likely – if nothing is done – that your baby will never get a green card. Child dependents lose eligibility at 21 years old; the current projections are pointing to much longer times than that.