The last time a Major Faction lost its Capital hex, the Admins at that time either had that Faction select a new Capital World/Hex or chose one for them. For those that don't know, I'm speaking of the One Sith after the Galactic Alliance invaded their Capital of Coruscant. If that still stands with the present team of Admins, all I see happening with this suggestion is that the invaded Major Faction would have a chance to move their Capital Hex towards the centre of their "cloud." Which would ultimately do nothing but benefit the invaded Faction, rather than tearing that group off the map like some folk(s) in this thread have implied.
It's an admirable thought, severing the head of a snake to watch the body wither and die, but I just don't see this providing any tangible benefit to Factions on the map.