I think the larger challenge is competing with the broad business value that Shopify provides — Its not just payment processing, but also email marketing, theme and API services, a app marketplace, shipping integrations, etc.

Wix/Squarespace, at least last time I checked, treated e-commerce as an add-on to their core service (building websites.) Square is a payment processor which with an e-commerce add-on, but is heavily templated.