This is a very strange analogy.
I didn't buy my credit card. I don't own it. The credit card is just a little piece of plastic, totally useless without the line of credit, i.e, the service provided by the credit card company, in stark contrast with my computers, which can be used quite extensively without the App Store.
The credit card company is not gatekeeping "access" to me. I can pay for things with cash, a debit card, a check, etc. If I choose to pay with a credit card, it's because I wish to take advantage of the specific features of the credit card, the primary one of which is the ability to pay for the product later rather than at the moment of purchase.