This makes it impossible to do blind review (review without knowing who the author was), which seems desirable. Do existing math journals do blind review?
I agree that blinding would be preferable, but when the material itself reveals the author it's simply not possible.
Usually people post their preprints to the arxiv at the same time as sending the article to the journals. This means the information (in a somewhat rougher form) is available immediately, and priority on an idea is established quickly. This has greatly sped up the development of mathematical ideas, but, yeah, essentially means one can search for the article being reviewed, and that double-blind review is more-or-less impossible.
OTOH, double-blind review is a great way to deal with conscious and unconscious institutional and gender biases, so would be great to have...