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.
Users of eCommerce platforms generally will be SAQ-A since they are not the ones controlling the system which handles CHD. This covers platforms like Shopify, BigCommerce, 3dCart, Volusion, etc, where the platform itself must be PCI compliant on their own, separate from whatever PCI level you are compliant with.
If you self-host, such as Magento, XenCart or some custom implementation - then yes you will be SAQ-D.
Your sales team walked away from the negotiations after a while because we weren't willing to pay significantly more just to have the brand "Stripe" be part of our business. It really was a "but, but, we're Stripe! AI! Why don't you just agree to the terms? AI!!! Did we tell you about the AI!?!?!".
I suppose it was Stripe's loss in the end... and I imagine we're not the only company that had this experience.
I have the impression Stripe's "bread and butter" are small-time shops (partnered with Shopify where 99% of sites generate < $1MM annual), hobbyists, and similar smaller operations that either can't negotiate better rates due to low volume, or don't know they can negotiate better rates due to high volume. Nothing is wrong with that - it just means Stripe isn't a good fit for companies with significant volume.
Does it? In my experience you can just use their Hosted Fields which are actually really great.