Not necessarily bad writing. Presumably they had the password for Vault 13, they didn't have the password for Vault 101 (or rather the one they had on file didn't work, since like I said, Amata changed it).
They had the password presumably for Vault 13 so they should have for the rest.
As I posted in my last post just after you quoted me lol. It would be a pretty big flaw in the Enclave's plan if the people in the Vaults could simply not open the door for them.
The Enclave would have the power to open any door on any Vault they damn well want. A backdoor password override code.
Colonel: "Men, the only hope for the Enclave's future is in that Vault. The dwellers have pure blood in their vains."
Soldier: "Sir, we have a problem."
Colonel: "what is it?"
Soldier: "They won't open the door and we have tried the all clear code, even asked them nice."
Colonel: "Well I guess we are royally screwed now."