I have only one issue with club tags.

They show who is not in the premade. Knowing who may be talking outside of game chat and who isn't is a huge advantage when ganking and roaming. Many times the premade focuses on helping their members more than the non-members and will tend to just back off rather than try and turn the fight or help them escape, leaving them to die. This is a huge advantage for the opponents because it shows obvious weaknesses and which lanes to gank (if jg) or where to press harder and try and make them (the non-members) fall very far behind.