As long as keys are never re-used it doesn't matter if the IV is predictable or not.
That depends a lot on the mode. CBC mode is vulnerable to plenty of attacks, if the IV is predictable. And what predictability means in this context has taken some people by surprise. If the end of the stream of data is not set in stone once you start encrypting, does that mean the IV is predictable? The way CBC has been used in SSL did have a weakness because of that. The cipher blocks sent across the network are used as IV for successive blocks. But once you have sent a cipher block, it is no longer unpredictable. And if the adversary can influence the next data block once he has seen the previous cipher block, CBC can be exploited.
This is the same tradeoff as when using block ciphers in counter mode.
It is true that counter mode is one of those modes, that do not require unpredictable IVs. In fact you can just use a counter to generate your IV. But if you do not choose IVs carefully, counter mode is one of the weakest modes, you can choose. If you ever reuse an IV, you have effectively reduced the encryption to a multi-time pad. CBC mode with a constant IV would be more secure than that.
The thing is, that counter mode is actually a stream cipher, which operates by generating a stream of bits, which is XORed with the message. All ciphers constructed in this way are vulnerable, if the IV is reused. That is exactly the problem with WEP.
I have seen at least one published article recommending the use of counter mode for storage encryption. It did not explicitly say you should use the sector number as IV, but it was hinting, that's what you were expected to do. Additionally using sector number as IV has been common practice in storage encryptions. Any storage encryption following that practice would be broken if an adversary was able to get the data which has existed at one logical sector number at two different points in time. Ways that could happen includes:
- Wear levelling on a flash/SSD medium.
- Remapped sectors on a harddrive.
- Access to earlier versions due to slight difference in alignment of write head.
- Encrypted data stored on an untrusted host or accessed over an untrusted communication path.
- Adversary with physical access to copy the encrypted media more than once.