They need to be in different trust zones unless your willingness to enter a credit card into any website means you’re willing to allow every other website you may be visiting to observe that input. Ditto viewing bank information etc.

That’s the point: you can’t just pile every website into the same zone, and if you did pile them into the same zone, then using a different password for x.com and y.com is to some extent pointless because x can observe y’s password input and vice-versa.

(disregarding the fact that in current computing architectures “just put all the untrusted stuff on one core” is probably an insufficient solution due to shared caches anyways, no indeed nothing in this attack requires “sharing a core”)