Using a non-random plaintext ID doesn't hurt your privacy (unless you publish it somewhere to link it to yourself), but reusing the same plaintext ID significantly reduces your privacy.
There should be no issue reusing an encrypted ID (the plaintext version, as in the integrated address) in the context of the Monero blockchain (this answer does not address any out-of-band concerns, like assigning your customers incremental IDs where they can tell what order # they are, etc.).
The key is a "random" one-time-pad, so the randomness (or lack of) of the plaintext doesn't matter. Knowing the plaintext ID and seeing the encrypted ID (revealing the key, as it is simple XOR) provides no additional useful information, since the key is used only for that particular transaction.
Since they are only 64-bit (space-saving), collisions of the "ciphertext" are expected to occur after about 5 billion transactions (with IDs). A collision also provides no meaningful information.
8 bytes isn't much room to include a message, though.