I think influence works really well as the resource driving your core empire expansion. Anything that adds more systems to your empire, more room for pops to live, or more base pop growth costs influence. Including it in diplomacy works well because diplomacy often effectively expands your power base by getting other empires on your side via federations, defensive pacts, commercial pacts, favors, etc.
I think the main thing we're lacking is worthwhile uses for influence that expand your empire in a "tall" direction. Things that makes planets larger and adds base pop growth the same way adding new colonies via system expansion or habitats do. We currently have some of these:
- Create/restore ecumenopolis
- Planetary prospecting
- Habitat expansion
- Mastery of Nature
- Ocean world expansion
However, they're a bit of a mixed bag. Creating an ecumenopolis is fantastic but only works on worlds where you don't want basic resources. Also, it doesn't really feel great to me to spam out ecumenopolises to get some extra pop growth; I'd prefer to only make one or two so that they're more special.
Planetary prospecting is random so it often won't give you a worthwhile deposit. It's also locked behind a tradition tree that always feels a bit lackluster.
Habitat expansion is great because they really need the extra districts, but naturally it only affects habitats.
Mastery of Nature and ocean world expansion don't strike me as that useful because you don't tend to totally fill up many planets. I generally prefer to stack the bulk of my population on ring worlds and ecumenopolises with the rest of my colonies having just enough pops to get the full base growth bonus. It's not hard to get to really high planetary capacity to reduce the needed population for maximum growth to 16-20 without needing extra districts. Adding a few extra districts to your one or two ecumenopolises that you actually want to fill just doesn't feel very worth it.
I think strengthening some of these options so they're more appealing influence sinks and adding some new, more accessible options is a great way to go. In particular, having a fairly repeatable way to add additional base growth to planets that costs influence would be great. It means you can add more growth to your empire without needing to add to your number of colonies. Being able to say, double the base growth on a planet for an amount of influence similar in cost to a habitat would add a nice option for people who want to expand upwards rather than outwards. Perhaps it could be 25 influence to add 0.5 extra base growth, which is then increased by the population/capacity adjustment and your pop growth modifiers. It could have a limit of 6 times so you can only double your growth on each colony, and maybe there's an ascension perk that increases this limit.
Planetary ascension could also be an interesting option for this if it cost influence and increased growth instead of only improving the designation (and now reducing sprawl). The increasing cost per ascension levels in your empire would have to be removed so it's more repeatable though, and it seems like they want this mechanic to go in a different direction.
