The enclave likes to think of itself as being the last remaining american government. Fallout 3 would have felt odd with some sort of other bad guy (see above ). It had been like 10+ years since the last fallout game.
It would not have felt odd with any other Faction then the Enclave. You talk about continity with other games but FO2 has the Enclave being destroyed. FO3 had to come up with a half ass reason why they should be in DC and never explained why they have so many in DC or why they have the downgrade in armour.
New Vegas does not have the Enclave, we have new factions Caesar's Legion and it feel way more Fallout then FO3 IMO.