Harbors existed as early if not earlier than Lighthouses. The fact that it's a medieval era building is just a game mechanic. Base Civ5 gives Carthage free Harbors and it made sense because Phoenicia/Carthage was known for its harbors. IIRC, the change to Lighthouse was done to preserve the free connections when that change was made.
I discussed the possibility a year ago, but I ended up just doing it myself for my own games. I replaced the free lighthouse with a free harbor.
Overall, from multiple games, I didn't feel it afforded Carthage any tangible advantage in terms of power.
- Harbors provide food to tiles but don't provide gold unless there's a sea resource which also provides +1 production. It's a nice tradeoff cause you both care less about not working water tiles if you don't have a resource, but you feel encouraged about working sea tiles when you do
- Harbors don't have instant connections, but now I actually look forward to research Sailing first to build the Lighthouses (thematic!).
- You trade the early snowball for a delayed power spike with really strong coastal cities, pushing the power spike to the Classical Era (yay also thematic). The Great Cothon benefits are unlocked around that time. You get the +3 production when it's actually relevant.
- You actually don't feel bad for building the Great Lighthouse, which has appropriate buffs for Carthage's paradigm, by accepting the effective production "loss" given by your UA.
- The bonus production to naval units actually felt relevant at that stage of the game. By the time you build Harbors in base VP you're just buying everything anyway. I shifted my focus to building naval units and purchasing land units (yay thematic)
- The bonus range to trade routes also felt appropriate for the civilization. If anything this was the best part of the whole thing. Rushing Sailing for sea trade routes and Great Cothon's extra trade routes actually felt very immediately impactful.
- I actually feel I want to choose between Authority and Progress now rather than only picking Authority if I feel I have no other choice.
- With this change, the impact of the uniques lasts all the way til late medieval, rather than abruptly falling off a cliff at early Classical.
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Ultimately the delays ended up somewhat muting the benefits of the UB change while removing a significant portion of the awkwardness that I always felt while playing Carthage. The only real issue I saw was the insane amount of free

. I never actually reached the limit and it could be effectively nerfed for Carthage til the Harbor tech is unlocked.
And honestly as an actual developer solution... can also quite literally just give them the
Cothon as a unique Harbor. It's not like the Great Cothon does anything mind-shattering on its own. The buffs it provides can be thrown in as tech unlocks to the civ/buildings, to ultimately surpass the default harbor.
Honestly just looking at base Carthage, it's comparatively uninspired for a VP civ. I feel it's only been tolerated because of how OP it can be in the right situations, which admittedly is why I enjoy it as well. The early game is my favorite part and I love coastal gameplay.
Still, I think changes can be made. Spain's on-settle bonus is much more interesting now. I do like the luxury idea posted above. All good. For now I'll just continue the swap for myself, but I thought I'd share an update.