Logistically how is payment made ?
I go to Target, pick the minutes card for the amount of minutes I need off the rack, pay for it in cash. When I get out to my car I scratch off the material hiding the code and enter the code into my phone. I throw away the used card and the Target receipt for it.
There is
almost zero trail tracing the transaction to you. The reason it is not a zero trail is that Target (and I would guess other vendors) has a video camera covering each cashier. My SO came home one day from Target and couldn't find something she bought (greeting card). She went back to Target, told them the cashier she used and approximate time of purchase. A employee went into a room behind the service counter and came back after a couple of minutes and said that the recording showed that the cashier accidently put the card into a bag by itself and my SO didn't take it - the bag was used for the next customer (based on the video they gave her a replacement). I don't know how long they keep the recordings (this is a lot of data to keep) or if the recordings are linked to transactions but other than some super agency like the NSA, I don't see how it is practical (or even possible) for local LE to trace back to you.
If this bothers you, just take a look next time you are driving and take notice of all the cameras that are literally everywhere at intersections (not talking about red light cameras). There are ways to reduce the data by orders of magnitude (that I won't go into) but there is still too much data to practically store for any significant period of time. This will change due to technology advances over next couple of years - IMHO, Orwell was only off by maybe 35 years.