What it does:

Cities that were created by independent people and all their attached territories get 10 influence per turn. (which is a very big bonus)

Why is it bad?

Conquered IP cities also count. (not only assimilated ones)

It encourages the player to detach territories from their own cities and attach them to IP cities. (cities you create become second rate)

It encourages the player to strategically create new IP cities by gifting outposts to wondering IP armies without land and then ransack their own cities and replace them with IP created cities (just to get the +10 bonus).

Proposal for change:

All territories that have foreign influence present (less than 100% domestic influence) should get the bonus (these are border territories and coastal territories with a harbor)

- this means that in order to get the bonus you need to share borders with other empires (which puts you at risk of generating grievances)

- if you get overwhelmed and your land falls under foreign influence, all those territories get the bonus (which will help you push back the influence)

- if you overwhelm your neighbor you lose the bonus because you would have 100% influence in your lands (which lowers your influence and gives them a chance to recover), and encourage you to switch to monoculturalism

- if you build your land in a ball shape, you would get almost no bonus (middle territories are 'protected')

- if you build your land in a snaky shape that shares many borders, all the land would have the bonus (but will be harder to protect)

Advanced:

- Monoculturalism could receive a bonus to make your territories easier to influence for yourself (your own territories receive double domestic influence), this would defend against cultural grievances

- Multiculturalism could receive a penalty (your own territories receive 30% more foreign influence), this would put you at risk of generating cultural grievances

Proposal example:

- green circle gets the bonus (attached territories and cities)

- outposts get no bonus

- 100% influence territories get no bonus

From what I get from your post, the exploit seems much more tied to the ability to gift an outpost, than to the civic.

The detach from your own cities to attach to a new one requires proximity and influence. To really exploit it, you need to put enough territories together to create a big city, which can create issues in the early game. The amount of influence earned is not that deciding later. Furthermore, the addition of the Embassy gives another potent influence generator, that makes this exploit less an issue.

Your solution is to generate more influence in your favour, while being overrun by foreign influence, so to fight foreign influence with foreign influence. It seems to go against logic.

My point is that the current implementation does not really make sense.

I attack an independent people city and the population dies in the defense.

So now this 0 pop city and all the territory I will attach to it will be considered 'multi-cultural'. Whereas all the cities I created don't get any bonus.

Also, you can destroy your own cities and create new IP cities in their stead.

I think switching the bonus to culturally contested territories makes more sense.

I do agree with you, on the diagnosis. It's only that I don't share the same opinion on the treatment.

“Culturally contested territories” are presented as clash of cultures, places where different way of living fight each other. That should not lead to a cultural boost.
I think that the game is not well suited to do it: it lacks the possibility to deal with population from different culture, to have a stabil religious minority, etc.

The way I see it, there's something of an heritage that gives a reason for the current form. Plus, there's still some population in the city most of the time, that would explain the permanence of this heritage.