You don't get a free client ruler when you build the type 4 government, you have to recruit one. They cost around 5,000 minai. Once recruited you have two choices: Leave him in the city and end turn and he becomes a puppet king, remove him from the settlement once recruited and end turn and he becomes a general. Type 4 government is very useful I think. Once you recruit a puppet king he automatically gets high influence and very often has quite a lot of +1 law and -1 unrest traits, meaning your family member and army can move out in 2 turns' time and carry on campaigning.

Type 4 government is also good for role playing. As you may have noticed the AI in RTW is abysmal. Allies will pretty much always declare war on you and send endless stack after stack after stack of troops at your cities. The type 4 government can stand in as an ally where the AI/diplomacy fails. Obviously you own the city and the land, but you have installed a puppet king there, you do not garrison your armies there but let your puppet king recruit a general and soldiers to be directed by you. In times of war he can send his troops to you to bolster your army on campaign, and he may recruit and lead troops in the province to put down rebellions from pesky freedom fighters resentful of your dominance of their land!

This is also what type 3 government can be used as. If you play as the Seleukids or Ptolemies for example, type 3 government is "loosely controlled satrapy" or something to that effect. It's like making the land you just conquered an ally and letting them more or less govern themselves, only interfering in their business when you need to demand they send levies and cannon fodder for the armies you recruit from your homeland (type 1 and 2 government) cities.

As for troops, type 3 and 4 gov't give the best selection of "foreign" levies. In most of the eastern half of the map the levies you can recruit are things like Pantodapoi, Persian archer-spearmen, Parthian spearmen, Median cavalry, Eastern axemen (they're particularly good), generally lots of lightly armed infantry and decent medium cavalry. That kind of goes for everywhere really. You'll never be able to build an enemy factions' best troops even witht he highest level of foreign natives' barracks.