It would be trivial for sketchy websites to have fake (but real looking) "official" Visa/MC forms, or even for multiple fake "official" sites to be set up. So redirecting everyone to the One True Payment System is no solution to fraudulent websites.
It is when a bank phone app is being used as a second factor (or, when on your phone, it redirects to it). This has been used in the Netherlands for almost 2 decades[1] for online payments (iDeal) and card fraud is basically a non-issue.
[1] Before smartphones a hardware token that requires your physical card was used.
