Great merchants and engineers are usually great. Great scientists are a bit worse, there are many quite useless (1 eureka etc.).
Given by how easy the combat is in Civ6, I'm not bothering with generals and admirals anymore. I mean I don't use their combat bonus ability, because moving them around with your army is tedious and you really don't need the bonus. So I always use their one-use ability (this may also be the reason why I skip some of them when the one-use ability is not good for me).
And musicians, writers and artists? In many games I avoided them, because I didn't want to get accidental culture victory (happened to me few times). On the other hand when I wanted to end a game and culture victory seemed to be the easiest one, I rushed them.
What I don't like with these 3 is that there is no alternate use as in Civ5. You even no longer get money for selling them. So if I'm avoiding culture victory, I often just destroy them and get nothing at all. I think there should be the option to sell them for money or for culture (selling for culture would make sense IMHO).
Great Generals are obscenely good. The most important is the extra movement (which they didn't have in Civ V). Secondly, they STACK. Not only does the +5 combat strength stack but the extra movement stack. It is terrifying when you have 5 movement Crossbowmen (with +15 combat strength) due to having 3 Great Generals.
Even when I have advanced past the era for a Great General, I find it more useful as a 4 movement scout, caravan protector, and fog buster, than wasting the General for a one-time use ability (or a unit I could easily purchase).
You can always create a Great Work and sell it to the AI. They will often pay lots of gold for it.
On the whole I think that the Great People system is simply amazing in Civ VI and I love how you have to compete for great people, it's such a good system. However, I firstly think that there should be more variance with great people and not just Sun Tzu all the time as the first great general. Secondly, as you pointed out, the fact that when you capture great people they mystically return to the owner's capital seems totally dumb. Surely you should be able to capture them?
? It is randomized which great people show up (and in which order). So Sun Tzu isn't always the first great general. Sometimes it is Hannibal. Sometimes it is Boudicca.
No thanks on capturing Great People. It is bad enough being able to capture Settlers (as opposed to Civ V when capturing a settler turned it into a worker).
I overall like the system, but it does seem to have some flaws for me. The biggest one is that in many cases, rushing for a certain type of great person will actually be in your disadvantage. This is most pronounced with Great Artists, where the early ones will give you religious art, which is actually in your disadvantage because it's very hard to get theming bonuses with these. The great engineers is another prominent example of the early ones being basically crap.
The other flaw, which is somewhat related to the above, is the fact that often when you pick a great person, you'll unlock another one which is much better, even from the same era. This for me is very bad game design, because it punishes you for being first to achieve something (which should always be rewarded in a game like this).
Theming is a mess.
But Religious Art is actually the easiest to theme in the beginning. You could theme Religious Art in the Renaissance or Industrial era. It is impossible to theme Portraits or Landscapes until the Modern Era, and to theme Sculptures until Atomic. The problem is that there is no more Religious Art after Industrial. Also, Religious Art can be stored in Cathedrals (my favorite religious building).
Uh, if you don't like the current Great Person being offered, you can PASS on him/her. That's the existing mechanic to ensure you don't get screwed earning a Great Person first (and getting one you can't use).
I really like the system in Civ VI. It is just great to compete. I agree that some Great Scientists are not good enough and I constantly earn Great Admirals on water maps that I don't use / want. And somehow passing on GP doesn't seem right to me. However, their movement needs to be cut down heavily. Only the rare ones that have abilities in far away lands (Darwin, the one that gives a luxury from some point of the map) should have 4 movement. The others can teleport anyway and thus 2 movement should be sufficient. I like that they are unkillable - it would be too easy to exploit for human players since you always know when and where a GP will spawn. If you could kill/capture the great prophet of another civ, the whole religious race would be useless. You'd always just wait for your neighbor to generate that Great Prophet and steal it.
The 4 movement is a logical result of the district system (which can be 3 distance away from your capital) and the requirement that many Great People need to travel to a district to use their ability.
Most of the time, when you earn a Great Person you can use them that turn. It would be annoying if you had to wait 3-4 turns (or more) to even use the Great Person because of its slow movement.
Whilst great scientists are boring, they are effective. I'd like the great artists/musicians/writers to have some form of passive or alternate abilities, similar to what they had in Civ 5
No, no, no. That would be bad, bad, bad.
In Civ V, there were lots of Great Writers, Artists, and Musicians but it was ultimately a limited number. Thus, I was sad when Great Works were forever lost because the stupid AI used them for culture, golden ages, or concert tours.
In Civ VI, there are even fewer Great Writers, Artists, and Musicians. I don't want to see the AI's destroying Great Works for such ephemeral benefits. I like how the AI's end up with Great Works and you can trade for them.
I also think Great Writers are the most usable of the three culture/tourism related great people. They don't need to be changed at all - giving steady tourism and culture makes cultural districts worth building and I like that the buildings in there are more or less worthless when they are not filled with writings or art or whatever.
I can even imagine a similar thing for the last building in the science district: instead of giving science directly, they could have place for a great scientist and you need to put the GS in there to get his/her benefit and some steady science income.
Great Musicians and Artists are another thing however. The shuffling around Great Works of Art is tiresome. Why not include much more artists that are cheaper but everyone just generates one piece of art?
I'm fine with archeologists though. It is a bit of work to get 3 or 4 themed museums, but it is doable and not too tiresome. I feel I'm often very lucky anyway when it comes to digging up things. I also like how other civs denounce you when you dig in their lands and take the artifacts with you.
Uh, I enjoy shuffling the Great Works around and organizing them.
I just wish there was an option to expand them for an golden age like earlyer civs.
If i dont find a use for them. Sometimes you own to many great generals/admirals.
Or a scientist that boosts faith which you dont have a good use for.
Maybe it would be good to get a discount for your first one. It is hard to compete if you are late for say culture or science. And there are 3/4 civs way ahead in the race.
As mentioned, I always have a use for Great People. Even ones with crappy abilities are useful as 4 movement, unkillable units.
I don't like the generals/admirals at all. They give a bonus you don't really need, you have to attach them, move them around, then they become obsolete. I actually prefer Civ IV great generals, which I alwyas put as military instructors in cities. Also, the way they were earnt in previous games (based on combat) made more sense. It synergised with how you played. It was simple, straightforward. Now it's bland, you have to pay faith or gold to get great generals instead of actually fighting.
I don't attach Great Generals. I just have them follow my armies around. They serve as useful scouts, can locate enemy troops, and can block certain units too.
Whoever says that Generals are a waste of time, it's because they never used their retire ability. You can have early access to powerful units with promotions and maybe a corps or amy out of it.
For example, combining all Medieval Era GG, you end up with a Knight Corps and 25% combat bonus for mounted units. 4 movement and 72 strength is nothing to sneeze at, especially that early in the game. But you need to invest almost everything into it: early Encampments in all cities and running Encampment projects instead of infrastructure. High risk, high reward.
While many of the Great Generals do have good abilities, I still think they are more useful as 4 movement, unkillable units that can teleport between your cities.
They serve as unkillable scouts, fog busters who ward away barbarians, caravan defenders who protect them from barbarian scouts, and teleporting blockers who can prevent enemy religious units from converting your cities.