I don't believe gorgeous or ugly UI came into consideration when we switched payment system for my SaaS to Stripe. Our main consideration were ease of integration, payments transfers from Stripe to our Bank, and User payment dispute resolution. I doubt it we ever check Stripe dashboard and use Stripe App since the integration. Only time we go look at anything on Stripe site is when we need look up something new we are trying to integrate or user payment related issues. I would love to know how Stripe users are using the dashboard and other UI oriented stuff beyond APIs. What values do these thing add to users' business.
However, the things you love about Stripe - like its ease of integration - likely come from the same dedication to quality and user experience that went into the design. Amazing UIs are often an indication of a well-thought out product in which a lot of time went into all the details, including UI and functionality.
A product that cuts short on presenting a polished product on the outside, may very well have the same ugliness to its internal components.
Or, as sometimes happens, 90% of the effort went into the design, and the product itself is crap. That happens too. ;)
