Is it possible to have placeholders (maybe PlaceholderAPI integration) in prefixes and suffixes? Among other things, this would allow the player's Vault prefix to be used.

As an addition to this, I think having placeholders for the user's display name and real name would be beneficial, assuming we get the ability to decide whether or not to show the user's nickname in future releases.

Yep! PlaceholderAPI has %player_name% and %player_displayname% placeholders - https://www.spigotmc.org/wiki/placeholderapi-placeholders/

I've discussed this briefly with @sgtcaze - I'm not opposed to this idea.

Might even get them to add in NametagEdit into PlaceholderAPI. :)

This has been added to v4.1.2 of NametagEdit. Commit soon.