Pretty much. Flagships don't necessarily actually engage in combat, nor are they even always well armed.
Now, I have no doubt that they could, and with their helicopters perhaps even be effective (especially since she had Super Cobras aboard at the time, and specialized units to carry out their missions). Still wouldn't be my first choice as a dedicated "Patrol ship," like was being discussed. As a Flagship and "operating base," for the forces she was deploying, though, sure, great choice. I'd still go with a dedicated Helicopter Carrier if I had my pick, but they could have done worse. Considering many of her forces at the time had cross-decked from the Iwo Jima, I'd say odds were that the Navy had thought the same, and when it was time for the Iwo Jima to turn back, they needed a replacement.
Also, I hate to bring this up again, but I did some math based on some realizations I had (mostly regarding how beautifully the Fibonacci Sequence fits into certain parts of these calculations) regarding ship-length-speed figures and their relation to water-resistance, factoring in errors. If the screws were the same and didn't provide any additional issues (and they probably would), you'd need at least a 1Gigawatt reactor to push out enough power to get a Nimitz going an additional five knots. Speed screws might help that, but again you're placing a lot of extra stress on the ship... but you'd be able to get a nice "rooster tail" of water coming off of the back of a carrier, which is a cool though.
I did, however, realize that this would also require upscaling much of the propulsion plant. It'd either get somewhat crowded... or require a bigger ship, which brings us back to ship-length-to-speed ratios. Considering the stress on the hull at these speeds, you'd have to increase some structural supports.
In short: Yeah, okay, I see why it's not logical to expect more than 30-33 knots out of a carrier. Just wanted to prove it to myself. Doubling reactor-power, essentially, just for an additional few knots that are going to cripple your ship anyway?










