Not according to Lucky Bancho's census. Balmung had 29,000 active characters prior to Stormblood's launch and has dropped to 22,000. While that number has inevitably slowed, multiple servers are catching up. So I sincerely don't they keep Balmung closed for four years.
Which was Lucky Bancho's. His use mounts, minion and achievements to monitor character activity. Levi and Cactuar come head, with Omega only at 15,000. SE probably has different ways they evaluate this however, hence why Gilgamesh remains locked despite having lost a considerable amount of active characters.