This creates lock-in with whatever company is storing the cards. Let's say you let PayPal store all your cards and you only had tokens. Now, you want to switch

This creates lock-in with whatever company is storing the cards. Let's say you let PayPal store all your cards and you only had tokens. Now, you want to switch to Stripe, but you'd have to re-acquire the cards from all your customers to do so. If you're doing recurring billing, you're going to lose a significant percentage of your revenue doing this, perhaps so much that it's not feasible to switch even though you're unhappy with your current processor.