> You need to have some protection against brute-forcing.
Yes, that protection is called "password".
> Whether it's limiting the rate of guessing or whatever, the attacker is still "modifying the state of a system."
Which is why you should not limit the rate of guessing (or at least offer that option--limiting the rate of guessing does help users who use terrible passwords, after all).
> Indeed, that's a weird rule. When someone stole my credit card number and ran up charges, my bank called me to verify them. How was that not "modifying the state of a system?"
Which is exactly why that shouldn't be a thing. Being able to pay with a semi-public number is just stupid. You should have to authenticate using a strong password, and "stealing credit card numbers" simply wouldn't be a thing anymore.