Forgive me for thinking I could skip a detailed analysis and speak generally and in hyperbole without attracting the ire of every civ4 apologist on the forum. But alas, the gauntlet is thrown, isn't it.
First of all, if these issues were really not a problem in Civ the correct response would not be to cite examples of specific games where this feature worked well. I can't say that jaguars are actually a great uu because there was this one game I played on chieftain difficulty on an Amazonia map where they totally dominated. Any such evidence would have to be based on broad and typical examples about Civ, not one random game where all the cards fell just right.
But even if we were to take your examples as typical of Civ IV as a whole, I don't see how they would make my (three) points "demonstrably wrong". For the banks, I admit I exaggerated: banks are not actually "pointless". However, as the article demonstrates, the only time you ever want to build them is if you can increase your research by doing so. And the fact that the slider is usually set at a lot more science than culture makes gold buildings much less effective for the cost than a similarly priced science building. I don't know about you, but I like to play games where I build banks so I can get more gold, not wring out some marginally beneficial research advantage.
As for culture, you will note from that link you provided that the players in question had 2 other great artist units they were saving to burn on golden ages. That in itself is a sign that there is something fundamentally wrong with the culture system when the best use for great artists is something that does not involve culture at all. But honestly, my main problem with the system is that culture only matters at borders; in interior cities all buildings that increase culture could just as well do nothing. It makes having a well-cultured capital deeply unrewarding. The fact that it's effective to rush culture in a bunch of newly conquered cities is a demonstration of that problem, not a rebuttal of it.
Finally, the battle results you linked to were so mind-numbingly boring I almost fell asleep at my computer. Perhaps there are people out there who have fun calculating win percentages in order to determine in what order their units should engage in to-the-death duels, but I am not one of them.
Honestly though, my point was never to get into some lengthy discussion about the merits of various civ4 systems. I was merely stating that the designers were fixing most of the things I had a problem with in Civ IV, and that I was happy about this. Whether those systems were good or not is honestly immaterial; I had a problem with them, and it affected my enjoyment of the game. To try and prove that I am wrong for asserting this is about as productive as to try and prove that I am wrong for saying I don't like how lima beans taste.
To everyone else; I know this is way tl;dr, sorry.