thats a good idea, however I don't like cultural influence anyway. It ruins the enjoyment of the game.... consider how much influence pamphlets and free radio ever had on populations in any war. Populations that were on the enemy side already that is.
I do believe that rather than using culture that negotiations could take place with the planet to see if a surrender, vassal or other arrangements can be made. These negotiations could be influenced only sometimes by the player who currently owns the planet.
e.g.
Planet gets attacked, like Aleraan it has no defences(even hardening) yet and none of its fleet are close by.
So they offer terms to the attacker. However they cannot offer terms until you have researched a new technology "mixed culture"
a) Some of its trade profits can be re-routed in exchanged for u leaving the planet un-molested.
This can be undone by an enemy capital ship arriving in the gravity well or strong culture. And will be a pain for the defenders to un-do.

They offer themselves up as slaves and surrender. Disbanding all orbitting installations and on-planet installations. The planet now comes with a slave\subject population.
c) They offer you control of all orbitting installations
This also allows you to build enemy ships from whatever installations are available at that planet.
d) They offer to allow you to build defences
you may now build planetary defences that will stop enemy ships intervening and slow down
their recapture
e) vassals\protectorate. the planet offers all installations and the population as a protectorate but does not release control of the planet to you. You gain all planetary income. this can be undone by a sizeable enemy force of ships arriving in gravity well or strong culture.
The attacked would accept terms if the odds that the enemy would come back while they were attacking the planet were good. Especially capital class raiders.
Once terms are accepted you cannot change your mind and blow the planet. If you do, no other planet will offer terms for a cool off period to simulate a lack of trust once your word is broken.
Proximity to the enemies capital planet would influence whether the terms were offered at all.
Un-affiliated planets would also be able to offer terms.!! Making it easier for passing fleets to waste less time conquering planets as they move to their main objective.