Pent-up demand for a PayPal alternative are from sellers who have a customer facing PayPal payment mechanism. Customers know they're paying with Paypal and customers usually have a PayPal account they use to pay you with. PayPal can hold on to customer funds like a bank.
With Stripe, a customer doesn't know you're using Stripe and if they had a Stripe account they wouldn't be able to see all the purchases they made at various sites that used Stripe, they're just not the same thing.
PayPal now owns Braintree, so they now do compete with Stripe.