I've always thought that lack of boosts on CLAIM bits was a bit odd, but then, the entire part is a special snowflake in many terms (no renewal, reduced lifespan, no boosts). Although adding boosts would be an interesting idea.
Increase the amount of ticks removed from an enemy claim when using attackController
Increase the amount of ticks added to a friendly reserve when using reserveController
Decrease the cooldown on subsequent attacks when using attackController
These three I'm all fine with, and don't see them breaking any game mechanics
Decrease the fatigue generated by claim parts
This one's kinda.... weird. Personally, I don't see much use for it, since just slapping more MOVE parts on the creep, or boosting them, would nearly always be more efficient and cheaper.
Increase the range of the actions enabled by the claim part
Now this one is a problem. A lot of code (for ramparts deployment, etc.) is built around the fact that any creep-controller interaction must be at melee range. This change would break it a lot.
All in all I think adding boosts to CLAIM parts might be an interesting addition.