Seems a bit convenient for Apple to leave no way of explicitly excluding the messages from the backup. Some people may want to keep their messages locally on the phone storage they own, but not care about messages enough to back them up. This leaves customers no choice but to turn off the iCloud backup altogether, or start a subscription like you mentioned.
I see no other reason to have this limitation other then coaxing customers, who may not want to be bothered finding out exactly what is eating their cloud space, into upgrading their space and paying more money to apple.
$1 a month is just the beginning. Even if that's all one buys, multiply that by the millions of iPhone customers with more then 5GB of messages, and your talking millions being earned because of this.
Is there any option available to automatically clean up photos and videos from the message app sometime after they've been viewed? Nope. There is only an auto delete retention time for entire message threads.