This is a really good point and you're likely to have the gold to make spamming those UIs across your empire pretty easy.
One thing I'm hoping to see get looked at in the future in general is town specializations... some of them just don't seem all that worth it as it currently stands. Buffing some of these means buffing towns, and that would buff Carthage. Fishing/Farming does what it's meant to do and does it well. Mining is decent, but maybe not for Carthage as do you really need extra gold? Their kit encourages you to use trading posts on one hand (Codex slots) but makes them pointless on the other (+15 naval trade range). I think if Urban Centers were better for culture and science production Carthage would be well setup to take advantage of it (and maybe that's where there Codex slot could go, instead?), but right now they seem pretty bad and I never bother.
One other thing to watch out for as Carthage is that I think they can get unlucky with map spawns with their coastal bias... make sure you don't have so many resources or mountains around your capital that you don't have room to expand your only city! This actually came into play in my last game as them with Isabella where I had ocean to the west and a mountain natural wonder to the right (comes with taking Isabella, which could be a bit of a drawback to choosing her in this case?), plus a smattering of resources nearby as well. I had just enough space to get by but it was pretty cramped and no way would I have been able to build multiple wonders there.