That's not how they pitched it to us - and I asked for clarification multiple times because of how absurd the proposal was for a well established eCommerce site. Sending customers off-domain for a payment is not something we were willing to do for a normal credit card checkout flow.

Even "hosted fields" is absurd (and by that I assume you mean an iFrame you embed), and would require redesigning significant portions of the checkout process.

That, coupled with their refusal to even match our existing rates, was really off-putting. The sales people made little effort to understand our business and pain points - they just wanted to talk about how great Stripe is and all the AI stuff they do.