In border areas with high culture pressure, border tiles will regularly change ownership. This will sometimes coincide with a normal border expansion of your cities, but will also regularly happen when the culture level (0%, 20%, 40%, 60%, 80%, 100%) of your city is stable. Such border changes are often the result of a long build-up of culture by both sides on the border and various buildings can push the borders in one direction and back again. All of these border changes will mess with the tiles that your cities can use and it takes quite a lot of effort to notice all of these won and lost tiles, especially on larger maps with many dozens of cities.
I would like to see a reminder that mentions when you win or lose tiles within the fat cross of one of your cities. This will allow you to adjust the tiles that your cities use. Preferably, this reminder would be mod-friendly so that if someone uses a mod where cities can use tiles at range 3, then the reminder will recognise this and giver alerts accordingly. The reminder would also notice when you win a resource tile (connected or not) which is outside of your cultural borders but can be used for its special resource benefit (once connected).
Given the huge number of options available (which can be overwhelming for newer users), I think it's preferable to capture all of this in one option, (both the tiles within the fat cross and the resources tiles reminder). I don't expect there to be players who'd want the one without the other.