TD:LR version
Please don't gut this great game based on poorly implemented ideas from possibly the worst game in the civ series

It took decades for them to get away from the SoD and actually make combat interesting in civ and now it has creeped back into civ 6 which is one of the main reasons it is so boring to play.
Long version
I also recently dabbled in civ 6 again and came running straight back to VP although one of the big factors for me not liking civ 6 was the souless and oddly micromanagy corp/army system. The way you upgraded to corp/armies meant you had to micro it to gain maximum benefit and then because you could essentially conquer the world with 5 units combat became souless and uninteresting. It wouldn't have been so bad it you could just pay gold to upgrade the unit directly rather than having to build fresh untrained units and take them to the experienced units to make it most effective.
This is probably clouded by the fact the AI is rubbish in civ 6 and often wouldn't build/rebuild military units so you could conquer the world with 5 units and i feel the corps/army system combined with the huge scarcity of late game strategic resources was really just a workaround to hide the poor combat AI and revert back to SoD in all but name.
The beauty of VP combat is, like
@Bryan317 partly mentioned, you can actually use and often need to use thought and strategy to succeed and while not perfect the AI does a pretty good job at combat.
War is also very varied and engaging where in almost every game of VP i end up in at least one epic battle which can happen over a small choke point, a huge front, be extremely fluid in open terrain, a long hard slog in heavy terrain, could involve two (or more) huge navies battling it out at sea, a massive invasion fleet battling coastal defenses, a city barely holding out under heavy siege, a city trading hands multiple times, multiple stalemates over multiple wars, breakthroughs with retreats back to the next defesive point or eventually a complete victory.
Depending on the war you need very different army compositions and promotions. For open terrain i will focus more on mounted units and getting the range promotion on ranged units. For heavy terrain i will focus more on front line melee troops and indirect fire.
For defense i will focus more on ranged units and skirmishers and picking medic promotions, for attack i will focus more on front line melee and cavalry type units that can occupy territoy and take punishment but be cycled out to heal up.
Civ 5 and VP in particular really made this system shine in civ although it was nothing new really with it being suggested forever with examples like panzer general being the obious reference point.
In civ 6 my city state allies would be enough to wipe out any military the AI civs had and were usually more effective and agressive than the actual AI civs and then i would just roll in my two melee and three siege to one shot every city in my path in a yawn fest. Only pausing occasionaly to allow war weariness to deminish for a few turns due to no actual combat taking place before carrying on the steam roll.
In one game i conquered every capital on a huge map in around 50 turns with two bombers (all i could support with my strategic resources) which i often didn't use as they needed constant rebasing to stay in range, two tank and three rocket artillery armies.
I did have a navy but only found one enemy ship so never used it and i stopped at one point as i was able to build GDR's and i had to stop to allow the GDR's to get to the front so i could play with them and let them take the last capital just to see what they did.
The only strategy i employed was trying to take cities in blocks of 4 so that they would pressure each other and prevent captured cities from reverting due to loyalty.
Stragely the only combat i found remotely engaging was the religious combat as it was aried dues to the different units and promotions available, strategies that could be employed to convert 'friendly' cities without actively converting them and annoying your friend and it involved more than 5 units. But it was heavily let down by mostly a micro management mess due to the fact you couldn't rename units to see what promotions they had, you had to go back to one of your cities holy sites to heal up and the most basic function of no alert/wake when enemy religious unit was near function as it was 'combat' so you had to post guards and cycle through them every turn to simply guard your borders even if playig religious defense.
If i was to change anything to make warring less tedious it would be to allow units to 'stack' to move so you only really need to micro the front line but when 'stacked' i would make them in effect a civilian unit with no defence so we don't inadvertantly create a SoD scenario. If the AI could handle this would be the main issue and one of the great things about VP is it always seems that nothing is implemented unless the AI understands it. The last thing we want is a whole AI army taken out 'in transport'.
Having said that though i tend to find most of the issues around moving units/too many units in wars are more to do with bringing too many unts than are needed for the situation so you have lots of units milling around behind the lines causing congestion.
The district system i found, like pretty much all of civ 6, an interesting idea poorly implemented. In general i found i just built the same districts in every city for most of the game. Holy site for spamming great people if nothing else (especially as religion was a micro management mess), campus because science is progress, commercial hub/harbour because gold is god and an entertainment district/water park as i had worked out you could guarantee 10 happiness in every city which was 4 districts. I would build a military district in 1 city to get the military engineers if i hadn't been warring (Ironically as the AI doesn't build military units they seem to build a military district and have a military engineer stationed in every city) and then for the very late game i would spam whichever remaining districts were most geared toward my chosen victory type although in the mid to late game most of my cities would just end up on projects generally spamming gold.
I find myself specilising cities much more in VP that i did in civ 6 apart from tradition games where the capital is just so powerful that it tends to be the main focus of everything.
It can be a bit less obvious in VP to specialise cities especially as many of the national wonders buff more than one yield but i find that interesting as you then get to make choices and while in the late game you probably will end up building most buildings in most cities, in the early-mid game i tend to prioritise certain types of buildings in certain cities to reinforce their inherant strengths from their location. City specilisation is more based around city location and terrain around them and boosting those natural bonuses which seems more natural rather artificially creating a speciallist city.