Well I mainly played 3, 4, and 5, haven't really gotten into 6 for various reasons, so I'll be talking about those mostly.
It's a mix of both not catching literally game-breaking bugs and also not realizing egregiously obvious problems that anybody who actually played a full game would be able to notice. Civ 3, 4, 5 all had major crashing issues on launch, but Civ 5 multiplayer stands out as being completely unplayable when it first came out due to the constant crashes, indicating it was very definitely rushed out the door with zero playtesting.
You had people making stuff like this:
https://www.change.org/p/2k-games-fix-civilization-v-s-multiplayer-now
With Civ 3, the major balance issue was that gameplay seemingly intended to favor tall play, with corruption making it so that cities more than 1-2 dozen tiles out from your capital suffered from so much corruption that they could never develop, but at the same time the lack of a penalty mechanic made it so that every single city added to your empire was a net plus no matter how little (due to corruption), leading to actual optimal gameplay consisting of furious landgrabs and very wide play.
With 5, well, where do we start? First off, on launch they balanced the game to hilariously favor wide play. City-state bonuses were per city while terrain tile bonuses were shit, meaning the optimal playstyle was to build as many cities as possible with no regard to where they were, which also made you militarily unassailable because cities now can attack too, so your Infinite City Sprawl doubles as an unconquerable continental fortress of overlapping fire. The CivFanatics guys realized this within about 3 days of launch and were posting playthroughs of them stomping Deity level AIs, when normally Deity level is supposed to be "if you play absolutely perfectly you can barely scrape out a victory about half the time". Then Firaxis realized that this was dumb, but then rebalanced things too hard in the opposite direction by buffing the empire size penalties to be crippling, so that the optimal number of cities was always 4, leaving huge amounts of the world uncolonized and barbarian-filled even into the modern era.
Then there were issues with the combat AI being just hilariously awful all around. You had players conquering entire AI empires using 3-4 horsemen because the AI could not comprehend two-move units that could attack and retreat on the same turn, which meant that they would live forever and rack up massive amounts of promotions. This led to horsemen getting nerfed hard early on (rather than, you know, improving the AI).
Oh and there's the weed they were smoking with diplomacy. Like, diplomacy is pretty bad in 5 even after the patches and expansions, but on release all the AIs might have as well been coded completely based on dice rolls, they'd declare friendship one turn and then insult you the next with no apparent rhyme or reason, then there's the fact that all AIs in 5 will eventually come to hate you no matter what, which AFAIK is still more or less true.
Just generally it's the kind of issues that would be solved by having a high-level player go through 2-3 games, Civ 5 in particular these issues were being noticed on CivFanatics within a week of launch, it's not like they were particularly obscure, you just needed someone to actually understand the game mechanics to play the game a few times.