In order to work with existing unmodified file systems, disk encryption must map plaintext disk sectors to identical-size ciphertext disk sectors (typically 512 or 4096 bytes), independently for every disk sector position. This excludes adding any state such as a counter to each sector.
That means when you overwrite a disk sector, you are essentially limited to using a disk-wide secret key and the disk sector number—neither of which changes from version to version of the disk sector. That pretty much rules out using a stream cipher, because you need a unique input for each version of the disk sector to select a different key stream.
In the worst case of the best possible disk encryption scheme, where every disk sector position is encrypted using a 512- or 4096-byte permutation chosen uniformly at random, an adversary will be able to tell when a disk sector is unchanged from one snapshot to another.
Modern disk encryption schemes like CBC-ESSIV are approximations to that which leak a little more than just which complete disk sectors are unchanged but not much more: specifically, CBC-ESSIV leaks which prefixes of disk sectors, in cipher block units, are unchanged. (BitLocker used to use the so-called ‘Elephant diffuser’ to better approximate ideal disk encryption so that it doesn't leak the prefixes either, but it was removed a few years ago for reasons that remain unclear to me.)
Aside: The utility of disk encryption is important, but limited. It thwarts a thief who steals your disk, and it lets you recycle your disk or send it in for RMA without having to worry about sensitive information that might have been stored on it. It does not thwart an adversary who can modify your disk: if it's in your laptop, the adversary has far more interesting avenues of attack than overwriting parts of your disk, e.g. installing malicious firmware.
For something like a remote disk, like iSCSI, where tampering is relevant, you might sensibly use an authenticated encryption scheme involving a stream cipher at the level of the file system rather than to simulate a disk that existing file systems can work with. For example, ZFS supports authentication in the file system, whereas a disk could not transparently add that for all file systems without risking serious data loss in cases that the file system would otherwise handle gracefully.