Credit cards are the definition of arbitrary debt. If the correct way to use them is to pay them off every month, and the only reason is for points/benefits, they are completely arbitrary. Just another way to profit off of people in difficult situations or those with weak willpower.
They also take a percentage of every transaction. Your 'reward points' came out of your own pocket in the form of credit card processing fees that are baked into the price of everything you buy.
Visa takes a cut from transaction, only a portion of that goes to the bank. I get 2.5% cash back on my transactions, but Visa only charges a 2.24% transaction fee. There must be more to cash back than the transaction fee.
It depends on whether the plan is prepaid or postpaid. Postpaid plans are the ones which establish a line of credit since the phone company is tracking your tab and asking you to pay it down at the end of each month.
With that being said, phone companies want as many people as possible on prepaid plans because why wouldn't they want to borrow your money every month? If you want postpaid you need to specifically ask for it and also pass a credit check.
I got my first credit card entirely to build credit and I paid off every transaction daily. I would classify that as arbitrary¹ debt as it is taking on "debt" for the sake of entering the system. I was much happier with a debit card at the time and still dislike having to pay it off every month. The cashback on my newer cards is nice though (didn't have that on my first one).