I think the government system itself is pretty limited the way it is. I like the idea of making it more robust or adding more features to it.
On the topic of governments, I think it would be better if governments actually reflected the system of governing that they employed. I've made notes on this but I never really got anywhere with them. Since you've brought up governments, I figure it would be nice to talk about them. (Sorry for getting a little off topic, I'll try to bring it back after).
Anyway, I think the flat government style that Civ 6 gives is too simple to be fun or useful. The governments are very strictly limited by era, and they don't reaally reflect how government truly function- governments are incredibly complicated. It is true that governing systems have increased in complexity over time, but it's false to say that every government in history could even be categorized into only one of the systems available in Civ.
I'd enjoy a system where instead of unlocking new types of government, you unlocked features for your government. Not policies, but attributes of the style of government. For example, an oligarchy is not really just a government ruled by a small group of people. If we wanted to look at the Ancient Roman government (after the Roman Monarchy, which predated the Roman Republic), we have a system where there are around 300 senators that make all the decisions for the republic. This sounds like an oligarchy. But each year, they elect two consuls or praetors to share power and control a veto. This sounds a little like a republic. Except when they didn't elect a consul and instead elected a solitary Dictator that had absolute power for 6 months. This sounds a little like an autocracy. You can't forget that the senators and consuls were always elected out of the patricians- the rich and ancient higher class of society. This sounds like an aristocracy.
Clearly, the Roman government had aspects of a lot of different ruling systems. A more fun and engaging government system would be one where you could select a very general form of government and then select sub-modifiers that specify how your government actually operates. [Note: these aren't policies. Policies are more like laws or regulations. If we compare a government to a painting, then the policies are the subject and form of the painting- the face or scenery depicted. The "sub-modifiers" are the paints and brushes. They define how you can convey an image onto the canvas but don't define what that image is] Each type of sub government attribute has advantages or disadvantages based on reality- we're not pulling things out of thin air, it has to make sense. For example, if you have a hereditary monarchy with divine right to rule, (which is basically what many monarchies in Medieval Europe were) you're a more effective leader when you have stronger faith output: it's the faith of your people that translates into their faith in you. That is your power. Divine-right therefore is much stronger if you can play a strong faith game, but also vulnerable if someone starts converting your cities: if the faith of the people changes, their faith in you changes.
Another type of government might be a Theocracy. This type of government implies divine-right, but instead of a King, you're lead by a religious leader. This person is probably elected and an example might be the Pope with the Papal states (although there were many city states in Medieval Europe that had their own Theocracies). A Theocracy should be able to spend faith points to buy buildings or units and can choose their majority religion regardless of the number of followers (which could theoretically block a religious victory) but would cause heavy amenity problems as your people revolted against a faith they didn't follow.
These are just examples, but I think it shows that there's a lot of room for a more nuanced government system. Governments would be constructed from a combination of attributes rather than a simple name, and the types of policy slots and the abilities that your government has are based on the combination of these attributes. When you add or drop an attribute, there's a penalty based on what that attribute is- if you had an Aristocracy for example, the nobility would certainly have a problem if you suddenly took away all their power. Conversely, adopting an Aristocracy in an age of high education for the common person would create civil unrest- educated and informed people don't like losing rights. Some government attributes would also favour certain eras- you could TRY to run a democracy where every person could vote in the ancient world, but if your people are uneducated (however that's measured), you end up with way too many uninformed voters making poor decisions. This would be a time that you'd want an Aristocracy- when the common man isn't qualified to make big decisions. But it's up to you how you govern yourself and the type of government you have.
ANYWAY, to try to bring this whhoooole thing back to the OP's topic: I like the idea of government dependant wonders. I think though that government types would have to be stronger for different play styles or victory conditions and more nuanced, and changing governments should have steeper penalties. Unless you do it gradually, major government upheaval is huge- think of the French and Russian revolutions or the fall of the USSR in the early 90s. It doesn't happen overnight and it's never easy.
