I tell you, ill fucking build a statue to person who can do decicive blow with culture cannon in big games
Step 1 attack somewhere with your fleet.
Step 2 shoot the battle with the deliverance engine.
You are now fighting in YOUR culture (there is no way to stop the deliverance engine shot from generating culture) which buffs you, and debuffs the enemy+ you get a generic extra combat buff specifically for being hit with the love gun. So to be honest i'll take the vasari having 10 % less attack power and me having 10 % more mitigation over a big explosion that does nothing any day.
Perhaps in a big map no rush for 12 hours you have 18000 kostura cannons which are admitedly more usefull than 18000 deliverance engines, but if you played an actual game you'll be lucky to get out 1 (NOTE 1) and the deliverance engine will be the most usefull in supporting your attacks, then the kostura then the novalith.
1 kostura is ok, it does the job (though not against starbases) and jumping behind their frontline is pretty cool.
1 Novalith is quite frankly pants. What decisive blows have you ever struk with that?
Secondly yes it does apply to all culture.
But you are always dominating the culture game having to invest less to attack than the enemy to defend, slowing his tech. Also you increase your allegiance and therefore economy faster than the other guys. Combined with advents maximum allegiance increases and, well considering you arent the 'traders' you have a pretty mighty economy.