The UK also makes company formation very easy and still slightly advantageous for sole traders, which may be a factor. I did check the criteria and they do include "must be listed for VAT or PAYE", so they're all real businesses to some extent and not just shells.
The US would do well to look at its business licensing requirements to see if they could be simplified in terms of paperwork.
There are quite a few non-legacy bank accounts that you can apply for a company account with in a very painless manner. Monzo, Starling and Tide spring to mind. I use Monzo as part of their business banking trial, but I previously have used Tide and (unfortunately) RBS.
Most company formation agents offer a free "bank introduction service". I have no idea how the logistics work, but I was able to open an account with Santander in a matter of minutes.
The US would do well to look at its business licensing requirements to see if they could be simplified in terms of paperwork.