More to the point, why were Nuneaton Town permitted to use the name of the old, defunct club? If you read their Wikipedia page it's quite misleading as it seems this Nuneaton side are the same one who were around in the 1930s, which isn't the case.
Allowing phoenix clubs to reclaim the history of previous clubs is a very dangerous game: it means clubs will no longer fear the nuclear option of liquidation and feel there are no long term consequences for being run into the ground. They can just start again as many times as they like, carrying on as though nothing happened apart from a pesky demotion. We all suffer as a result of this kind of irresponsibility (and indeed may ourselves become victims of unscrupulous owners).
And if this is FA policy now, what the hell is the point of forcing new clubs to change their name in the first place?