The problem with forbidding volunteer moderators from joining is they're usually just normal users who dedicate their free time to help out the site - they're not usually official representations of a site like an Admin would be.
I guess it would be like banning people who volunteer at charities from being able to enter the raffles. It's not usually a ban because you want to reward people who volunteer their time to the site, not prevent them from enjoying the "fun" parts of the site and only locking them into the un-enjoyable aspects of the site (moderating).
If maybe if it was an official position, like they were being paid or signed a contract, then it'd be something they can agree to, but right now there's no benefits a site moderator has compared to a OG Vet, besides they get more responsibility and have higher chances of getting in trouble. It would suck if we took away a community event from them because they decided to help the community.
With that being said, I do think weekly is too often. I've explained this on .com before when people asked me to change the voting system of MotM, but I don't want to dedicate an unnecessary amounts of my free time to hosting events like that. Doing it weekly would just become too much, especially if we're having a system where I have to read a bunch of replies and see if they're counted as "valid" or not.
I can create weekly trophies that are automatic that would be based off of certain statics (activity, post, rep, etc) but it'd be without human input mainly, and I assume a lot of the users don't care about the trophy system.