There have been tricks over time to do this, but companies normally realize the error of their ways and fix it quick.
Examples: Target redcard(I think) let you deposit money onto a debit card using a credit card, and this debit card had bill pay functionality so you could pay your mortgage/student loans with it. I don't believe it's an option anymore.
There was another pre-paid card, I think with Greendot, that you could load at Walmart using a credit card, and it also had billpay functions.
So they occasionally pop up, but normally not for very long.