It's not common. I was on a call with a group of Indian contractors and one of them announced they were relocating to the USA. The cheers on the call were insane.

From an employer's point of view it's easier to stick to X countries as the source of H1Bs as the process overall can differ between countries.

It's because statistically they are just almost entirely from India. There are a few Chinese ones but it's no where near the amount of Indian hires. Chinese H1b candidates are post graduates from PhD programs and are less common but make up the 2nd largest but still extremely small group.

I agree with this but I’ve found that the people making the decisions of who to hire usually have some incentive to hire from a certain country.

Those reasons could be kickbacks, family stake in the company, etc.

Edit: This is completely anecdotal. Grain of salt and all that.

For quite a while, H1B had been almost exclusively for foreign graduates from American schools so the distribution of H1B workers is as same as the distribution of foreign students.

In tech or IT, the ones who hires are mostly indians so mostly prefer to hire from there, I think even in Canada international students acceptance process, there were some complains that the majority of these students are from India.