There are many assumptions in your question, and most of them are often not correct.
The messages cannot be intercepted.
If this is true then you simply don't need cryptography at all, your communication is already secure. You use cryptography when you're not sure that it is already secure.
The messages cannot be altered
If this is true then you don't need a MAC. However, generally, if messages can be eavesdropped then they can also be altered. This is called a man-in-the-middle attack. These kinds of attack are for instance very feasible if you connect to a public Wifi network, as there is little to no authentication of the access point.
The message content is fully secret
Generally, it is not. We often have a good idea about the structure of a message, and we can often guess where the data is.
We can generally see when a message is altered
This is often not the case. If the message is altered at a point that doesn't generate an error then it will likely be ignored and passed as regular data.
Even if we can detect it at some point, we generally would like it at an earlier stage, when receiving the message. Imagine you get a complex message that needs to be parsed after it is received received. Now the parser throws an exception somewhere deep down the tree. What did just happen? Was the message generated incorrectly, is there an error in the parser or was there some attack? It will be tricky at best to distinguish one from the other.
All the above points really have nothing to do with an OTP. They are equally valid for any unauthenticated cipher. The fact that OTP provides perfect confidentiality has precisely no influence whatsoever.
Generally we want our cryptographic schemes to detect any error in any message. In other words, the chance that a bad message gets through should be negligible. For that, you need at least 128 bits of security. It is unlikely that you can get that kind of security by just looking at the contents of the message.
Generic encryption schemes try to achieve security for any kind of message. So lets see what happens if we simply generate an example of a single bit message.
The contents of this message can certainly be confidential, using just one bit of key stream. However, anybody can see that flipping the bit of resulting ciphertext will result in a message with exactly the wrong content after decryption. Therefore an OTP will provide exactly zero bits of security when it comes to integrity/authenticity.
Even if you hash that single bit with SHA-512 and include the hash then an attacker can flip exactly those bits required to get a flipped bit with still a correct hash when parsed. This is why a MAC requires a key to be used.