They don't immediately change alliegence, they just give the target planet a massive boost to the culture rate (whether it is on your or your opponents planet). Fire it at a planet with no culture buildings to see how much (though it is effected by the number of phase lanes connected to the planet). I find it useful for firing at my front line worlds, so that my culture can reach the enemy's border worlds. If you research the tech that gives you line of sight with your culture, it can even be used as a good spying tool.

Still, I consider them the worst of the superweapons. However, in entrenchment they now give a damage bonus to your ships in the gravity well they fired on, so they have some combat use as well.

Maybe it could increase culture on your planet, and spread non-culture when it hits enemy planets (i.e. red enemy phase lanes indicate culture, once advent superweapon hits, the normal grey starts spreading from the planet instead, stopping after a certain amount of time. then the phane would be culture-free. don't think replacing it with your own culture would be fair, though.)

OK, here's an interesting idea.

The Advent superweapon wouldn't destroy enemy culture centers--it would reprogram enemy culture centers at the planet that is hit and any that are connected to that gravity well, taking them over, turning them into your culture centers with your maximum culture rate spread bonus (30%).  The enemy would have to go destroy them.

I find that if the enemy has no culture, or very weak culture, the Advent cannon can wreak some real havoc.  However, if the enemy has strong culture coverage and it is teched up, the cannon's culture effects are minor and are rapidly shrugged off....even when you fire a few at one time.  It does cause some economic impact and convey a culture bonus to you in that gravwell for a brief time, but against strong culture the effect is so small that I am not sure it is worth building a chain of cannons.

Considering the amount of havoc or economic impact you can cause with 2-3 TEC or Vasari superweapons, the Advent cannon seems a bit weak.  Of course, everything else about Advent kicks butt, so I'm not ready to cry for them just yet!!!

+15% damage to Illum spam is underpowered??

Does the 15% bonus apply to strike craft and structures?  How about to allies?

Can you imagine the use of this thing in team games if it does?   That means your econ guy can give a 15% boost to ALL team members. 

I personally love the advent superwep, late in the game when I have 10+ of them I just set them on autocast and watch my enemies economies get obliterated, much more useful in the long run then straight up damage