Not sure why you would want this feature. Most banks have an auto pay feature for your monthly bill.
On a personal level, I log into my frequently used credit card accounts every 2-3 days and pay them all off,
but there's not much advantage in doing this - can help to keep your credit utilization at zero and make
sure you don't overspend. But not sure you'd want it to be compulsory.
Maybe it's personal preference...
I read a few comments asking why would I want this feature. I like to monitor my daily transactions, and not be surprised by the charges when the monthly statement is arrives. Maybe I'm just a control-freak!
You could use a debit card since that is essentially what you are asking for (there are many that give 1% cash back). The alternative is something akin to text alerts on every transaction and a running total. Mint and other tools can also help but again, the point of credit is to monitor your spending and be responsible with it.
I'm not trying to be flippant, but if you are a control freak, it's hard for me to understand why you would want to use a debit card in preference to a credit card. Particularly should there be any fraudulent activity on the card, you are much more "in control" and much less at risk of loss if you use a credit card rather than a debit card.
I get called and emailed promptly when there is any suspicious activity on one of my credit cards. The major credit card issuers seem to have very sensitive software to detect fraud. Also, your liability is limited in the event of fraud.
The only account I've ever had real difficulty with fraud was a debit card. First, the bank's software never detected it. I was just lucky that I logged on to my account and spotted the fraud within a few days of its onset. Then it took several frustrating months and many phone calls to resolve it.
Today, I assume that every merchant where I use my credit cards will sooner or later be hacked. So I strongly prefer using credit cards. I don't want anyone getting my debit card number.