I have exactly the same setup with a major national brand-name bank. Works great. But one hell of a lot of Americans choose to bank with small town banks, credit unions, etc., which generally lack these features.
For some of the variable bills, e.g. my credit cards, the creditor can even send an “e-bill” directly to the bank telling them how much is the minimum payment and how much is the full pay-off amount and the due date. Once I’ve pre-approved “Pay in full X days before the due date, not to exceed $Y”, that all happens every month without intervention. But again the money flow is still push and I can turn that off reliably at any time.
But of the dozen-ish credit cards I use regularly, only about half of them are able to render e-bills to my bank. For all the others, I get an e-mail and I have to go to the bank’s site/app and manually order it to “pay card X $Y on date Z”. And do the same process again next month. and the month after and …