As someone else who also doesn’t hate Civ VI, I hope you don’t mind me answering your question.
Personally I enjoy Civ games for exploring and understanding how the game systems work. Not to the extent of min-maxing everything to a 150-turn spaceship victory or whatever, but rather in looking at the game design, considering what the designers were probably trying to achieve by a particular decision, what works and what doesn’t, what emergent strategies there are. This is interesting (to me) for most games where there’s not one right path to victory but multiple competing requirements, the best of which is dependent on the particular game situation.
So coming from that perspective, I’d say to take a look at the way the game systems intermesh, particularly the ones brand new to the game rather than inherited from Civ V.
For example, the research boosts system (that Tom disliked so much). I feel it produces a number of interesting effects, some good, some bad. The foremost of these is the way it acts as a brake on the progress of the research leader (without feeling punitive) by making them spend extra science / culture if they can’t achieve boosts to match their science rate. In turn this provides a pleasant positive reinforcement to the player who can manage this: when they have to work hard to get particular boosts and they manage to line them up at just the right time for the research.
On the minus side, it can act to limit available strategies by making any that don’t chase boosts inefficient. Also, some of the individual boosts are poorly designed: either too random, trivial to achieve or, worse, force you to do actions that provide no other bonus to your civilization and are just a production sink. And of course the AI can’t handle the boosts effectively, so in single player they act as a huge bonus to the player alone.
In a similar vein, here’s a rather longer description of the knock-on effects of the One Unit Per Tile system (written for Civ V, but still largely appropriate). Credit for this goes to Luddite from the Realms Beyond forums.
Hidden due to length
They wanted to keep the “civ” feel to the game, where you settle new cities, build improvements and city buildings, and go in to the city screen to adjust your citizens. This meant that they had to limit the total number of tiles in the game, and so they tried to force army sizes to be very small [to avoid traffic jams]. A typical civ 4 army of ~50 units would be incredibly annoying to manage in the Civ V style, so they wanted to encourage armies of only 5-10 units.
In order to do that, they had to limit production. You can see that in the decreased yields: production and food yield have been decreased compared to civ 4, whereas the food required to grow a city was greatly increased. The early units like warriors don’t take very long to build, but the cost of units quickly increases. The high upkeep costs for units, buildings, and roads factors in to this as well. The idea was, I think, that every new military unit would take about 10~20 turns to build, just enough to replace your losses while you continually upgraded your original army. As a result, your army size would stay almost constant throughout the game.
So now the developers are stuck with a game that has greatly reduced production values. That’s fine, except for one thing: what do they do in the early game? They can’t expect us to just sit around clicking “next turn” for 40 turns waiting for our worker to finish, or 100 turns for a library to finish. It’s bad enough that it already takes up to 15 turns to finish that first worker. So, they had to make the early stuff a bit cheaper. You can build a warrior in ~6 turns, and you can build a horseman or a library in ~10. Even a coloseum only takes ~20. The idea was that a small city was efficient enough to produce the early game stuff in a reasonable amount of time, and as the city grew, it would produce the later stuff in the same amount of time - keeping army size constant while the cities grew and built infrastructure. There would be no massive increases in the power of a city with its size (like civ 4 had) because if a city became really powerful, it could create huge armies which would break the 1UPT system. If large cities were only modestly more powerful than small cities, the army sizes would stay small.
What the developers overlooked was that we’re not limited to just a few large cities- we can build as many small cities as we want! Granted, we’re limited a bit by happiness, but there’s a lot of ways to solve that little problem (like keeping the city size small). And since small cities are so efficient at building the early game stuff, and large cities never become vastly more powerful, the many small cities with their trading posts (even without any multipliers) will quickly outproduce the large cities with their mines, despite their forges and workshops.
The game is in an awkward situation where large cities can’t be too good because it would imbalance the middle and late game, but small cities have to be good or else the early game would be boring.
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Anyway, I hope that gives you some ideas. I’d also recommend playing multiplayer if you can find committed people of an appropriate skill level to play against (and ideally someone to make a balanced map). So much of what’s wrong with Civ VI lies in the AI; against competent opponents most of the design holds up well, providing interesting decisions and satisfying combat. Though it does start to fall apart later in the game, after the renaissance or so.