can Protocol specify "variable defined on class, but doesn't have to be explicitly annotated ClassVar"?

[kurtbrose]

Appreciate the help if anybody has ideas. Here's a minified example of what I mean:

from typing import Protocol, ClassVar

class ClassWithFlag(Protocol):
    flag: ClassVar[bool]

class TrueFlag:
    flag = True

class FalseFlag:
    flag: ClassVar = False

flagged: type[ClassWithFlag] = TrueFlag  # error: "flag" is not a class variable
flagged2: type[ClassWithFlag] = FalseFlag  # not error

Both mypy and pyright give the same error. I understand the logic that ClassVar is stricter than just "variable on the class": it also means an instance isn't allowed to overwrite the value.

I wish protocol implementers didn't have to provide the ClassVar annotation.

Should I get rid of the type and just have a protocol that applies to the class instead?

class HasFlag(Protocol):
    flag: bool

flagged3: HasFlag = TrueFlag

But, that can't be combined with TypeVar -- there's no "and" combination of types, so I can't say "this is both a TypeVar AND implements the Protocol".

Closest related other discussion I could find was this: #1056