With regard to your first paragraph, I don't think there are any American universities that admit students by advisor. As far as I'm aware, your admission is a decision made solely by the graduate admissions committee. Even if you have an advisor ready to take you on the most they can do is recommend you to the committee, not supplant it. When you're admitted there are still criteria aside from research to work on.
I think this is a fundamental difference between American and European universities. In European universities, you can hypothetically join a PhD program without any prior degree at all if an advisor chooses to take you on personally. No such sidestepping can happen in an American institution, and regardless you'll have to take some courses (even if you're only auditing them in effect) before you can begin research. Unsurprisingly, American PhD programs are longer.
I think this is a fundamental difference between American and European universities. In European universities, you can hypothetically join a PhD program without any prior degree at all if an advisor chooses to take you on personally. No such sidestepping can happen in an American institution, and regardless you'll have to take some courses (even if you're only auditing them in effect) before you can begin research. Unsurprisingly, American PhD programs are longer.