On it's face these both seem like good traits, but it has two major glaring blockades that stop them from being useful.

1) If you build too many cities it sends you straight into bankruptcy.

2) If you do everything possible to not go bankrupt, you get huge cities full of pissed off citizens, which sends you into bankruptcy.

Also, the flip of it is that Organized and Financial are OP AF.

What am I missing here???

In Civ 4 each city is initially an investment. You need to pace your expansion balance your economy so you will be able to support your new cities until they become profitable. A common milestone is to aim for six cities, either settled or conquered, by 1 AD (of course, circumstances might change depending on the hand the map deals to you).

Overpopulation shouldn't throw you into bankruptcy. An unexpected and very efficient way to deal with it during the early game is using slavery in unhappy cities.

Now, on to the traits:

The thing about Imperialistic is not getting more settlers, but getting them faster. One turn can make the difference before settling a contested city spot or losing it to a neighboring civ. Your cities will be back to producing (and growing) faster. However, after the initial land-grabbing period, its usefulness is limited. Faster Great General emergence is nice but not game-changing.

Expansive, on the other hand, I'm very fond of. There's no such thing as too many workers, so faster worker production is good. The bonus health becomes useful at higher difficulty levels, where unhealthiness is a real problem and not just a nuisance. And double production speed for granaries, a building that you will want in every city, is superb. Faster harbors are OK if your civ is coastal.

If you are going bankrupt, I suspect you are neglecting the economy. By all means, it's possible to get into trouble by expanding too fast in the early game, when your economy can't keep you afloat, but typically only on the top difficulty levels (Immortal, Deity), because maintenance costs are higher there.

A typical opening consists of:
* build worker first (seems counter-intuitive at first, but try it out)
* research the worker technologies you need (ignore religions, they're a trap)
* improve your food resources with the worker you typically get in turn 12-15 (depending on where you settle, and possibly Expansive trait)
* get Bronze Working and Slavery fairly early --> whip away unhappiness, ideally on settlers and workers
* get out two settlers early, so you have 3 cities by around 2000 BC
* build cottages in your capital, especially if you have grassland river or those 3-food tiles (I've actually forgotten what they are called, it's been too long since I played, haha)
* keep working these cottages as your capital grows
* (bit more advanced) found cities with Big Fat Cross overlap with the capital, and use these helper cities to grow cottages for the capital. The capital can't grow fast enough to work them all, especially with a luscious river-rich site
* gradually tech up to Civil Service for the Bureaucracy civic. If you have invested into cottages in your capital, the capital will now be a behemoth for science and gold (depending on the slider setting). Even with 10 cities, it's not uncommon for the capital to carry 50% of your economy

PS: With focused play, it's possible to grab Civil Service with the Oracle, even on pretty high difficulty levels. It's not something to aim for as a beginner, but perhaps you want to try it out down the line.

Throughout the development listed above, you gradually build more settlers and workers so you keep expanding the empire while taking care of the economy. And remember to improve food resources first. Always. (Okay, there may be rare exceptions now and then, but let's ignore that).

Of course you can try to rush a neighbour as well, but it's not necessarily as straightforward as it sounds. It's kind of a "all-in" strategy, at least on higher difficulty settings where the AI is capable of building a decent chunk of defenders (they use whipping with slavery too!). An Axeman rush can be tricky to pull off, but certainly possible. Horse Archers is easier, but requires Horses of course, which isn't a given. They move twice as fast, which helps a lot. Makes it easy to "fork" cities, which can throw an AI defense into disarray.

I'd suggest to focus more on building up the economy while peacefully expanding with settlers. You can try more aggressive approaches later. Building a solid economy is essential on all difficulty settings, and in most types of games. Unless you want to kill the map with Horse Archers or something. Then you can kinda ignore it and rely on capture gold =)

I think that I'm struggling with money because I expand too fast. I'm playing with a CIV3 mindset to get as many cities as possible, and I really need to focus on getting gem cities.

Definitely; there's a fine balance between territorial acquisition and killing your own economy. Even to this day I don't always get it right. It's easy to get too greedy and see your tech output sputter for a few centuries while you correct course.

Definitely. And it's why Writing and Currency is so important.

Honestly, many say Currency is the most important tech in the game, and I tend to agree with them. Once you manage to limp to Currency, all your woes are gone. Suddenly you can sell techs for gold, you can sell resources for gold per turn, and most importantly, which is what can save an economy in deep shit: you can build Wealth in every city if needed.

The extra trade route in every city doesn't hurt, either. I'd say it's as much the combination of Currency and Code of Laws that really causes everything to balance out. City upkeep is cut in half at about the same time as you get a whole bunch of wealth generation options, and that just opens up the game from that point onward.

The extra trade route helps too, especially if you happen to have some offshore islands. But the bigger benefits is the ability to sell cheap outdated techs for gold, and building Wealth. That is useful throughout the entire game, and can quite easily net you several hundred gold when you get Currency, and can start selling off Priesthood and other crap to all the AIs. Often means you can go 100% research for ~50 turns.

Courthouses can be good too, certainly. But be careful with them, and don't build them all over the place. They are very expensive builds, and in a small empire they are not worth to build. A rule of thumb I've seen bandied about is that once a courthouse would save you 4 gold per turn (so city maintenance is at least 8 gold per turn), you can start to *think* about it.

They become better in bigger empires, or in cities far from the capital (or Forbidden Palace or the relevant world wonder). And ofc, they are definitely needed if you plan to get corporations, because those put city maintenance costs through the roof.

It's what is both so good and sometimes a bit frustrating with this game, because so many things come down to "it depends" :D Sometimes doing X is a very good move, and sometimes it's a terrible move. There are very few hard and fast rules of thumb that are always good (or always bad for that matter).

Well, the RNG is always bad. Of course :D