This assumes that something like their e-mail address is static: in the real world it isn't. Normal users often use e-mail addresses assigned to them from their ISP, school, or work, and think nothing of the fact that these are needlessly transient identifiers. In practice you simply cannot automate the problem "I forgot my username/password".

(EDIT: Oh, and I misunderstood your comment: no, you cannot have them initiate the request with their username, because they probably also forgot their username. I thought you were saying that they could initiate a request to look up their username before looking up their password, which has the "no stable identifier" problem I ended up going into.)

Unfortunately that is even tougher for users to remember as there is even less context.