When doing a payment integration what would be the reasons the payment gateway would require your bank credentials instead of redirecting the client to his or her bank website?
The context of my question can be found on the Personal Finance & Money where I asked something different but regarding the same payment solution, i.e. Trustly.
With this payment solution you need to add your bank credentials on someone else's site (not your bank's). I was reluctant to do so, researched the site, asked that question as reassurance, even changed my home banking password afterwards. So my question is not about trust here (I kind of figured out they can be trusted although I still have a trust issue with it), it is about reasons why one might chose to do an integration like this.
Are there any benefits (technological, user experience, business reasons, others?) to do an online payment integration by asking users to login to their bank account inside your application?