And this is exactly why I do not understand why there is such a huge opposition against 3D Secure. It prevents this exact issue. Card fraud on 3D Secure pages that are well implemented (2nd factor with SMS or hardware device token) is non existent.
Here in the US, users avoid Verified by Visa (which I believe is the same thing) because it moves the burden of fraud onto the end user. Whenever that VBV page comes up, I immediately abort. I don't trust companies to keep my card data safe, so if the burden is suddenly on me, I'll just go without whatever I was going to buy if I can't get it elsewhere. It's that big of a deal. This is before we even get to technical issues or the UI/UX flow.
That's misinformation. It only shifts for 3d secure transactions work require another info that is not sent to your merchant. So the only way this fails if your bank had a bad 3d secure page or your fucked up.
Unfortunately it's a lot like Denuvo DRM - it hurts legitimate customers/sales too much to be useful.