The famous poet "Anon" died many years ago; a shame because he or she wrote many good pieces. A come-back is long overdue.
Imagine a world where magazine submissions had to be anonymous in the way that competition entries are. Administration would be more tedious but at least the selection process would be fair. Indeed, in an ideal world any magazine that didn't adopt this policy would be viewed with great suspicion. However, editors would then have to depend solely on their aesthetic judgements - a brave thing to do. Worse still, subscribers couldn't be favoured. I suspect that this change would lead to a wider range of authors being published (Ashbery imitators will have as good a chance of publication as Ashbery himself). The famous might be less keen to send their work in - one of their clearest advantages would be gone. Perhaps people wouldn't renew subscriptions to a magazine with fewer big names even if the poetry's no worse. The balance between magazines and books would change too - even more than nowadays, books would contain many poems not good enough to get into magazines.
Rather than wait for the world to change, anonymity can begin at home. If submitting under false names and addresses doesn't appeal to you, you might instead encourage your local poetry workshop to deal with anonymous poems. Try not to make it into a guessing game; concentrate on the text. If you can't distinguish members' poems from the minor work of famous people, don't worry - the difference might be smaller than you think!
PS: Since writing the above in Jan 2003, Anon has been released - "only the submission and assessment procedures are anonymous. A poem that is accepted for publication will go into the magazine under the name of its author... Rejected poets can remain anonymous"