Okay, I think I understand. You're being extremely harsh in how you consider brokenness, so if it's broken it might as well not be generating anything at all, no state needed.
I was considering "fairly broken PRNG" as its own significant group, and those need state too if you treat them as separate from "this literally gives the same number every time". But if those all go in the same bucket, then the comparison you made makes sense.
I was considering "fairly broken PRNG" as its own significant group, and those need state too if you treat them as separate from "this literally gives the same number every time". But if those all go in the same bucket, then the comparison you made makes sense.