The issue becomes verifying the passwords, then: supposing you have a CBC mode oracle, like a HSM, how can you verify two passwords are the same? (This is probably the reason they chose ECB mode in the first place.) In fact, if you allow the user to test if two ciphertexts represent the same plaintext --- and nothing else --- you still break the very definition of secure encryption, namely that a secure encryption scheme should have, as one popular definition, indistinguishable ciphertexts (usually under a chosen-plaintext attack).
So you have to develop some new way to measure security for the scheme, or perhaps somehow measure the damage that an equality oracle can inflict upon an IND-CPA secure scheme. The notion of indistinguishable ciphertexts roughly reflects the inability of an attacker to reliably learn any function of the plaintext from the ciphertext. Throwing that idea out the window seems unwise, since it's such an elegant idea. So, anyway, you're off in uncharted waters, not a good place to be if you're securing users' passwords.
All of that is relatively complex, though, so just let me know if I need to elaborate on some idea more. (I am never sure how in-depth to go in these posts.)