Why do online banks have this permanent residency requirement in place?
First, not all banks have this requirement, but a great many do. When I was a non-permanent-resident worker I got an account at a local credit union specializing in people in my industry.
But your question is why banks have a residency requirement. Let's follow the chain of logic:
- Banks are in the business of providing banking services.
- Criminals are particularly in need of financial services such as money laundering.
- Prosecution is a disincentive to crime.
- Foreign national criminals can, they hope, escape the consequences of crimes committed in the United States by fleeing to a different country.
- Online banking, not tied to any particular geographic location, is particularly attractive to money launderers. See in particular the "wire money abroad" portion of your question.
Or, let's look at it from another direction:
- Having a credit history, or otherwise being established in a country -- having a solid record of employment, payment of debts, and so on -- is evidence against the proposition that a potential customer will engage in financial crimes.
- Recent immigrants who are temporary workers have no such history.
In short: a temporary resident with no financial history is, comparatively, a huge risk of resulting in an expensive prosecution compared to a permanent resident with a long history of good behaviour.
Now, you might reasonably point out that the vast majority of H1B visa holders by definition have legitimate jobs that were vetted by the immigration process, and you'd be right. But banks are in the business of managing risks, and some of them have decided that the benefits to them of banking slightly-higher-risk customers does not make up for the increased risk.
Put another way: big banks are already making tons of money all the time. They don't want or need your business.