The accredited investor standard is higher then a basic test.

The standard may be higher, but the implementation is "This is what it means to be accredited: are you accredited? By the way if you say no, I can't sell you the thing I've been trying to convince you to buy."

If you had to take and pass a test, that might filter out more people; although I'm sure the seller would help you pass the test, so maybe not.

GP didn't say test. They said "self-reported knowledge [about yourself]". Which is correct.

the accredited investor standard is, a checkbox

its purpose is simple. if you lose the money of sufficiently powerful people, as a middleman, the standard exposes you one more kind of legal jeopardy.