"The Voice" has a pretty complicated relationship to the past, probably because there are multiple "pasts" in the poem. There's the distant past, in which the woman was "all" to the speaker (i.e., they were totes in love), and the more recent past, in which the woman was "changed" and she and the speaker were no longer in love. The speaker doesn't just wish that his beloved were alive; he wishes that the woman of the distant-past were alive. So there's this almost double-mourning in the poem—a mourning for the dead woman in general, and a mourning for the "changed" woman she was in the recent past. We get the feeling that the speaker wishes he had worked on his relationship issues before it was too late. (But death comes for us all in the end, whether we've gone through couples therapy or not.)
It's silly for the speaker to mourn for the woman of the distant past. There's really only one woman in this poem.
The speaker is being realistic by mourning for the woman of the distant past. People change, and he didn't like who his beloved had become in recent years. Time is complex, man!