There aren't many major US banks that will do this for you right now unless they're actually not banks and in fact prepaid card users that explicitly do not have a bank charter.
This is because online account opening for banks is a very hard problem, and anyone with a bank charter basically can't use the closed loop trick that other services are using to provide money movement and storage without a charter.
Once you are past account opening, it's more about tech politics. No major US bank has publicly pushed an Oauth gateway, for example. But this is more about risk and the politics of contracts with financial aggregators than anything else. You can find hints of these murky waters in the articles surrounding the recent dust up between Chase and Intuit.