My analysis factors that in. The fact is that AF GBs are much harder to level than PE GBs. For example, the cost to the owner to level Traz to 10 is 3140 FPs, and AO is 4216 FPs. The extra 1076 fps are repaid in 107 days by the returns from the AO. On the other hand, those 1076 FPs could be put to another use if desired by players.
This is a great point. Once a non-GvG player with an Alcatraz meets their needs for troops and happiness, their is no benefit to continued leveling. In contrast the AO continues to get stronger. Unfortunately, the gains are marginal (.2-.3% chance per level). Yes, the FPs increase, but the payoff time just gets longer and longer. [It is important to note that payoff time vary drastically if you power-level GBs, but that doesn't apply to 99% of players, so I'm using non-power leveled timelines]
Great question, hence the importance of play-style. Don't forget to account for the space-saving benefits of the Traz for most players.
I don't normally use them, but most players do...again this depends on the player.
**edit**
Ultimately, if you're going to GE at a high Age/Era you are going to want both an AO and a Traz. On the other hand, if you camp in Iron Age you can complete GE without either. The lower the age you camp, the more I recommend an Alcatraz before an AO because; a) the goods are cheaper, b) it's cheaper to level to the point you need to finish GE, c) it saves more space than an AO (assuming you need barracks and/or cultural buildings, and most importantly d) because it enables you to auto-attack much more easily, it saves much more time than the AO.
The reality is, at lower ages, you need neither. I was finishing IA GE with +42/+30, and I may have lost four units.
Again, with regards to the forge points, you don't need to put those 1076 towards the AO, since it doesn't have to be L10. Your base assumption is they have to be the same level. I could easily argue that the AO with the same amount of points is considerably more powerful than the Traz (or the reverse, depending on GvG), and arbitrarily saying they need to be the same level isn't really a strong argument.
On the other hand, the happy wheels fall off the Traz after L10, whereas the passive for AO slows down immediately after L10, but then slowly accelerates. Happy for Traz goes down and down, and then down. It's that way for most, so I'm not singularly criticizing it.
Saying it's cheaper to get to the point where you finish GE is completely unsubstantiated. I completely disagree, because it doesn't really help win battles. AO does. Traz will NOT help you win that battle you just can't win. AO can, if it makes its appearance pretty dramatically. And you can do your first turn and surrender if you don't get the results you want.
With regards to the small percentage, you have to multiply that by the number of attacks you'll be making over both waves. .3% might not seem like a lot, but let's say you make 15 attacks, there's a 4.5% chance JUST THAT LEVEL will cause a hit. If you're fighting two waves, it's probably going to be closer to 30 attacks, or 9%. But, I think .3% is high, let's even go to .25, it's still 3.75%, or 7.5%. And you know how important those hits are. But, then, there are many that don't matter (you'd kill it anyway for example), so it's not as earth shattering as those numbers indicate. But, it's still really powerful.
I've never needed the Traz even at higher levels, but I desperately needed it for GvG. So, I don't think it's necessary at all, and if I really needed some rogues, I could put up camps rather than waste the FP on the Traz. There's no way to otherwise approximate the capabilities of the AO.
I think the average 'casual' player might need happy, but I'd say Hagia is a better choice because it gives about the same happy per square, and gives something everyone needs more of, FP. Troops? I never do, and I only rarely build barracks. Many other people won't either. Even then, all these new special buildings have massive happiness, so I just don't think it carries much value anymore for dedicated players.