You can do it while your fleet is busy elsewhere. It forces your enemy to build cultural buildings to stop you, or park capital ships there. Races all also have some technology to give them a bonus while inside your culture, so if you spread your culture to an enemy world and then you invade, you're at an advantage.

It's not the strongest weapon in Sins (guns are), but Cultre can cause all kinds of problems for people if you use it well.

And it's very satisfying to see the entire map covered in your colour

it seems that the advent have more of an edge culture-wise..........

Mainly it allows for faster conquering of the planets and the ability to on Really large maps playing as Advent with the culture cannon they have to kill the economy of your enemy from afar( fewer planets= Less cash flow). also on the larger maps it allows you to concentrate your conquering forces and not need to include the very expensive and useless in actual combat siege frigates needing only a colonizer and a fleet to mop up any lingering defenses.

This is true.  Each race has an advantage over the other races.  For the Advent it is the culture side...for the Vasari it is the phase side.

Yet that information is harder to take advantage of in those kinds of games when Vasari cannons can put out production lines and TEC can destroy an entire colony off the face of a planet.

Destroying production is more effective imho. Culture simply can't be used (effectively) in the mass number of games online.