This is exactly what you should be doing with puppets. The main strategic reason to puppet is to keep the conqueror from suffering from massive amounts of unhappiness; if the conqueror is swimming in surplus happiness, then they
should be annexing the city. It's especially likely that the city can support its share of the science/culture burden, so that concern should be alleviated as well.
What's left is the player not wanting another city to micromanage. Players have been using puppets as a way to get out of micromanagement, but I think this should be alleviated in a more complete way: by giving the player the option to assign the governer control
of any city they own, where it focuses on buildings that improve the city's focus (but not prevented from building other buildings once the priorities have been met).
Then, puppets would be forced to use the governer and their focus cannot be changed.
If your choice is between eliminating the enemy civ from the map and vassalizing it, I think there should be pressure towards vassalization, so this is fine. The world doesn't want you to have vassals, and it likes it even less if you eliminate the civ entirely. It would much rather your enemy keep its sovereignty and the cities you were thinking about vassalizing/puppeting, but that isn't the choice presented here.
Vassals only give you
Culture,
Faith and
Science. They actually cost you
Gold, as you have to pay the vassal = vassal's
^0.8 + 10% of the vassal's unit maintenance costs. You can choose to recoup some of that money in taxes.
One of the big problems with puppets at the moment is they seem more of a left over rather than a definitive aspect of the game and i am not sure it is clear what their purpose is meant to be any more.
Puppets seemed like they were originally added in the base game as they really wanted to make a real effort to curtail ICS from being the dominant strategy and going tall always being the poor choice but had severe issues with a conquest victory style where by necessity you need to have a large number of cities even if you burned everything but the capitals which you can't and the often practical necessity of having to take other civs cities to secure basic resources or to cripple them to such a condition they were no longer a threat and if you just burned the cities they would just spam new ones so they invented puppets as a way of playing quasi tall or ICS lite if you needed to take additional cities with them giving you minor yields while allowing you to control territory and defend yourself effectively.
The addition of vassals supplanted many of the reasons for puppets and having a vassal is vastly superior as they are fully autonomous, defend themselves and provide high yields while completely guarantying they won't ever attack you (never seen an instance of a vassal demanding liberation and the AI only seems to go for global liberation if you have multiple vassals at which point you should generally be taking iron fist from autocracy anyway) and provide high yields in both simple tributes/taxes as well as guaranteed trading partners to sell your excess good to as well as send safe trade routes and if you leave them strong you get high yields from trade routes so you can leech extra science and culture from them as well as sign secure and effective research agreements.
I have looked back through my saves and have found two saves at different periods of the game to show how good vassals are.
Example 1
Mid game with 3 vassals spending 81 on vassal maintenance and getting 152 from vassal taxes so a net gain of 71 gold.
I am also getting 87 science, 64 culture, 42 faith and 15 happiness directly from vassals.
If we exclude the happiness i am getting 2.4 yields per gold spent from vassals
My cities are generating 540 science, 328 culture and 313 faith at a cost of 692 gold for buildings therefore i am gaining 1.7 yields per gold spent from my cities.
Example 2
Late game example with 6 vassals spending 597 on vassal maintenance and getting 1160 from vassal taxes so a net income of 563 gold.
I am also getting 1611 science, 2181 culture and 249 faith directly from vassal plus 26 happiness.
Again excluding happiness i am getting 6.8 yields per gold spent.
My cities are generating 4005 science, 2429 culture and 558 faith at a cost of 3324 gold for buildings therefore i am gaining 2.2 yields per gold spent.
I tried to keep it as fair and basic as possible but there are obviously numerous other factors but it clear that economically vassals are amazing assets and more so if you keep them large, the mid game example i had two vassals with one city and one vassal with 5 cities as the first two hadn't had time to grow properly before i vassalised them.
The late game example i had a couple of small vassals but i had two vassals with 9 cites one with 10 cities and one with 16 cities. I had taken the policy which buffed their yields but even taking that into account the acquisition of larger and stronger vassals in arguably better as in the late game example i am gaining over 3 times the yields per gold spent from vassals as i am from my own cities.
My conclusion from these examples is vassals are vastly superior to puppets as you get huge yields from them while making a profit in gold and actually gain happiness while they don't increase you tech, science or tourism cost and allow you to remove a threat while protecting your borders. I would even say looking at those numbers, which i have never done myself before vassals are even superior to actually owning (building or annexing) more cities even if you just want straight yield and don't care about the additional cost to science, culture and tourism.
On puppets specifically, an important question is what is the vision for puppets, are they just meant to be a quick in between phase to get less unhappiness while resitance ends and then you annex them so they don't end up costing you more unhappiness and if so what use are they for tourism gameplay at least which is the only real style that going wide really has a negative impact. Does that mean going tall is officially dead and tourism victory is always playing with one hand tied behind your back as you either have to stay small and weak or grow big and make your victory condition much harder?
I regularly watch diety lets plays and to a great degree they are kind of boring as they always end up going authority and warmongering but then there is the realisation that is the only way to compete on higher levels, expand, create vassals and annex everything even if your not going full conquest victory. Going tall/keeping puppets simply doesn't cut it and it seems this is so obvious even the AI knows it as i don't remember the last time i saw a AI puppet city where as a couple of years ago if the AI had been on a huge conquering spree a large portion of the cities would be puppets.
Puppets used to be a integral and necissary part of the game now the only time i keep a puppet is very late game and i am just working through to the end and i really don't care anymore.
There is something wrong with the tall/wide balance and i feel that if going wide and warmongering was brought back down again and/or puppets were made more useful and not just a general drag on your empire then puppets would be more relevant and tall would be more relevant also.
Culture, 
Faith and 
Science. They actually cost you 
Gold, as you have to pay the vassal = vassal's 
^0.8 + 10% of the vassal's unit maintenance costs. You can choose to recoup some of that money in taxes.
