Here I was not carefully enough. For clarity, I think that a public key must be uniquely mapped to the entity who is the subject of the certificate. There may be entities who have more than one keys. Because, the relying party that validates the corresponding signature may argue that he does not know who has signed the data. I would argue that a PKI that does not detect the certification of one key under several identities is weak.
Weakness means that the issued certificates are less meaningful for relying parties.
Anyone can do this. I beg to differ. This has successfully done with a least one well known CA provider. As a result, the certificates issued by this CA provider are less meaningful. Basicly, I agree.