This just goes round in circles. Admins can delete unsourced or attack articles based on BLP concerns. This can then be reviewed. The review should be closed based on consensus, not votes. But consensus is subjective, people judge it based on who they think has the stronger argument. Those who feel that the article should be deleted think that the consensus is to keep deleted for the BLP issues; those who feel the article should exist think the consensus is to undelete it, because the fact the article is sourced means that BLP isn't an issue. Both sides seem utterly convinced that they're indisputably correct, and spend most of the time talking past each other.
As I see it, at some point the goal of being a perfectly neutral encyclopaedia and the goal of not being dicks can't coincide; the dispute is over where the line should be drawn.