One or two culture structures at your front lines are usually all that's needed, maybe plus one on your HW initially.
Sometimes the AI isn't even smart enough to protect its planets with culture structures either, but if they're on the higher settings, they'll have already completely filled out their logistics capacity, and are too dumb to scuttle their other structures. So you might be overthrowing their planets every 10 or 20 minutes, and then they'll recolonize when one of their caps pushes your culture back for a bit, they'll fully upgrade the planet, they'll lose it to culture again... etc.
Funny, but quite aggravating when one of your allies happens to be an AI and is too stupid to protect its planets with culture.
LOL i beat an unfair ai vasari with an economy made up of culture temples boosting resource and tax revenue , crusaders,guardians,illums 1 capital ship (Mother Ship).
single player is a joke
One way to increase the difficulty is to refuse to build any starbases, forcing you to rely on your fleet.