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Walls are a bit different; walls don't automatically recover, and can't be repaired unless you hold off on the attacks for a few turns.
Corps and armies ... a Corps is not more effective at attacking than two units attacking at the same time. It's actually less effective if they're not hitting back; +10 strength is about +50% damage dealt. So turning four individual bombards that can all attack into two bombard corps doesn't actually help - unless you bring up more units into those newly vacated tiles to add their own attacks.
Large cities do also get intrinsically tougher; a city's defense strength gets bonuses for every district and every layer of wall. And the capital gets even more bonus strength.
And it often does just take a long time to batter down walls. You only get through walls quickly when you have a truly overwhelming advantage.
All of this is to say that if you're attacking a well-built city late into the game, then it will take a while. You need a technological advantage. Bombards aren't going to cut it at the stage of the game you're in. You need Artillery.
Just before I upgraded I had the city down almost 25%, I sent in my 3-buff line infantry unit to see how much damage it would do and it did almost nothing and died instantly! Then I noticed he had a cavalry corps. I checked the stats and he had over 90 strength, I looked at my other line infantry with 2-buffs and it had over 60. I figured I could survive that easily. I guess not. I expected at least 50% damage, not instant death.
A city's combat strength is equal to the melee strength of that civ's most powerful combat unit. So, until you get spearmen or swordsmen, your new cities will have a strength of 10, because warrior strength is 20. The capital is 13, because the palace gives +3. There are other bonuses to city combat strength, like unpillaged districts and being located on a hill, but they aren't percentage bonuses, just small flat increases, +2 or +3, which thus tend to be more important the earlier in the game.
If a city has a wall, it gets to make a ranged attack. The strength of this attack is equal to that of a civ's most powerful ranged strength.
The other big effect of walls is,of course, that they create a layer of outer defense that keeps the the city itself from taking much damage at all until and unless the walls have taken significant damage. Walls also create a -85% penalty to the melee attack strengths, which is not 100% , so it isn't invulnerability, but damn. If your units are an era or two ahead of the defenders, they can just brute force the best defense your victim civ can put up, but that's what it takes, an era or two ahead.
Short of being this far ahead -- and if so, why are you still bothering to conquer cities? -- if the defenders have walls, you need at least one workaround. One such workaround is provided by rams for ancient walls, then towers for ancient and medieval. The other workaround is the siege line of units, which do avoid that -85%, and take no damage from attacking. Siege artillery units do, however have wimpy defense strengths for their era,and the city's ranged strength tends to be directed at units with wimpy defense strengths. Getting extra range mostly solves the wimpy defense strength problem for siege artillery
Finally, the holy grail of city conquest, the bomber, arrives. They don't completely end the arms race because the urban defenses of a civ that has a mech infantry or modern armor army are pretty stratospheric, so even bombers do wimpy damage, at least until you promote them to jet bombers. Then, your victim might acquire GDRs, which are quite good at air defense. All that said, this late in the game, even on Deity, the AIs aren't usually going to be this advanced, so bombers enable the end-stage of unstoppable city conquest.
So, sure, your bombards eventually ran into trouble doing significant damage to cities. I imagine they worked quite well earlier. Then, you upgraded them to artillery to match the defender's upgrades which had made your bombards no longer work too well,and your dominance in the arms race was reestablished. Unless this is the last civ you want or need to conquer, eventually your artillery won't work well enough, so you will have to upgrade them to stay competitive. Finally, you will need bombers if you still need to conquer at that point.